Measurements are usually introduced as probes of quantum systems, but they can also act as a powerful, intrinsically nonunitary control knob for manipulating quantum states. This thesis develops the theory, experimental realization, and detection of measurement-altered quantum criticality in one-dimension: the phenomenon where local measurements on critical wave functions reshape universal long-distance correlations, entanglement, and other scaling behaviors. We show that measurements generate defect or boundary perturbations in the underlying conformal field theory, producing new measurement-induced fixed points and new universal observables that are often invisible to the pristine theory.
\r\n\r\nIn transverse-field Ising chains, we design measurement-altered criticality protocols in which correlated ancillas are entangled with the critical system and then projectively measured. This setting shows that measurement basis, entangling gate, measurement outcome, and ancilla correlations can qualitatively change correlations in the system and induce outcome-dependent order-parameter condensation. We also develop nonstandard probes --- including higher moments and symmetry-resolved averages --- that retain nontrivial signatures of the post-measurement ensemble.
\r\n\r\nThese ideas are then connected to quantum information by studying imperfect teleportation of critical many-body wavefunctions. Teleportation errors can be reinterpreted as effective weak measurements acting on an otherwise faithfully teleported critical state. This perspective yields a classification of protocols in which imperfections either preserve universal correlations and entanglement scaling, continuously deform them, or destroy long-range entanglement while leaving altered power-law correlations behind. Measurement-altered criticality therefore becomes not only a fundamental phenomenon, but also a tool for understanding and optimizing noisy quantum-information protocols.
\r\n\r\nWe also broaden the framework to measurement-induced boundary physics. In a gapless parent of the one-dimensional cluster state, a single round of measurements can generate boundary conformal field theories with distinct universal properties. Rotating the measurement basis drives transitions between these boundary fixed points, producing measurement-induced boundary transitions that have no analogue in the descendant gapped cluster state. Extensions to tricritical Ising and three-state Potts criticality show that such transitions arise generally in 1+1D conformal field theories.
\r\n\r\nFinally, the thesis addresses experimental access. We propose practical protocols for observing measurement-altered criticality in Rydberg atom arrays tuned to Ising and tricritical-Ising transitions, where projective measurements of selected atoms can controllably modify critical correlations with experimentally favorable post-selection probabilities.
\r\n\r\nWe also develop a post-selection-free framework for extracting nonlinear observables from raw measurement records using statistical learning. By recasting higher moments of conditioned observables as supervised learning objectives, the method replaces exponentially costly sector-by-sector postselection with regression whose sample complexity is controlled by decoder capacity. In critical Ising chains, linear, logistic, and convolutional decoders recover measurement-altered scaling and correlations from simulated unpostselected data.
\r\n\r\nTogether, these results establish measurements as a practical and universal route to engineering, diagnosing, and exploiting new forms of quantum critical behavior.
", "doi": "10.7907/t6m9-8h16", "publication_date": "2026", "thesis_type": "phd", "thesis_year": "2026" }, { "id": "thesis:17311", "collection": "thesis", "collection_id": "17311", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05302025-180056920", "type": "thesis", "title": "The Enemy of my Enemy: How Disorder and Dissipation Can Be Your Friend in Quantum Systems", "author": [ { "family_name": "O'Brien", "given_name": "Liam Christopher", "orcid": "0000-0002-8603-1347", "clpid": "O'Brien-Liam-Christopher" } ], "thesis_advisor": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "thesis_committee": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Nadj-Perge", "given_name": "Stevan", "orcid": "0000-0002-2394-9070", "clpid": "Nadj-Perge-S" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In many physical quantum systems, disorder and dissipation are a nuisance that must be actively countered or minimized, or something that the utility of the system must otherwise survive. In this thesis, we study how these typically harmful concepts can actually be helpful in the right circumstances.
\r\n\r\nWe first study disorder-induced localization in quantum systems---so-called \\textit{many-body localization}, or MBL. MBL suppresses the spreading of information, an otherwise ubiquitous phenomenon, and thus can be leveraged to preserve information and realize new types of protected quantum order. We discuss a novel mathematical technique to measure a localization length in MBL systems and connect this length scale to the conventional picture of the MBL-thermal transition. In doing so, we are able to probe the probability distribution of the coupling between distant degrees of freedom near the transition, which contains valuable information about the nature of the MBL phase and the transition to thermalization.
\r\n\r\nWe then switch gears and study how to harness dissipation for autonomous quantum error correction of Gottesman-Kitaev Preskill (GKP) qubits in superconducting circuits. Typically, dissipation destroys quantum information via decoherence, but we show how, by appropriately constraining the dissipative dynamics, dissipation can actually \\textit{prevent} decoherence and counteract the effects of noise. As a result, our proposed GKP qubit enjoys exponential robustness to extrinsic noise and imperfections in the circuit/protocol. We also demonstrate how to realize robust non-Clifford gates on our proposed qubit, granting our device universal, self-correcting single qubit logic. The experimental realization of such a setup, which we discuss in detail, would represent a major step forward for the field of quantum computation.
", "doi": "10.7907/mz8m-an97", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:16776", "collection": "thesis", "collection_id": "16776", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10072024-102144911", "type": "thesis", "title": "Microwave Spectroscopy for Probing Electronuclear Modes in Quantum Magnets", "author": [ { "family_name": "Libersky", "given_name": "Matthew Murray", "orcid": "0000-0003-4140-360X", "clpid": "Libersky-Matthew-Murray" } ], "thesis_advisor": [ { "family_name": "Rosenbaum", "given_name": "Thomas F.", "orcid": "0009-0008-6152-666X", "clpid": "Rosenbaum-T-F" }, { "family_name": "Falson", "given_name": "Joseph", "orcid": "0000-0003-3183-9864", "clpid": "Falson-Joseph" } ], "thesis_committee": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Faraon", "given_name": "Andrei", "orcid": "0000-0002-8141-391X", "clpid": "Faraon-A" }, { "family_name": "Rosenbaum", "given_name": "Thomas F.", "orcid": "0009-0008-6152-666X", "clpid": "Rosenbaum-T-F" }, { "family_name": "Falson", "given_name": "Joseph", "orcid": "0000-0003-3183-9864", "clpid": "Falson-Joseph" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Crystals with rare earth ions present an opportunity to explore a range of model magnetic systems, allowing for an experimental realization of several important physical concepts. For example, the compound LiHoF\u2084 is a transparent, insulating crystal which implements the transverse field Ising model (TFIM) with the Ho\u00b3\u207a spins. The TFIM is a well-known model which is one of the simplest systems to display quantum behavior, such as quantum phase transitions (QPTs). This makes LiHoF\u2084 very useful for investigating these and other quantum effects. LiHoF\u2084 ~also has strong hyperfine coupling to the nuclear spins, which means the excitations must be considered as composite of electronic and nuclear states (i.e., 'electronuclear'). This introduces a nuclear spin bath which modifies behavior near the QPT. In this work, we investigate the behavior of this QPT by probing the electronuclear states in LiHoF\u2084 at microwave frequencies. To accomplish this, we develop the use of loop-gap resonators which enable sensitive microwave measurements in LiHoF\u2084. We also extend the techniques to related systems, such as the 2-dimensional XY antiferromagnet LiErF\u2084. We then investigate ways to observe new phenomena in the LiHoF\u2084 system, namely improving superconducting resonators as one possible way to observe the dynamics of quantum quenching through the QPT.", "doi": "10.7907/n5w4-ae93", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:16640", "collection": "thesis", "collection_id": "16640", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:08152024-132609600", "primary_object_url": { "basename": "Caltech_Thesis_final.pdf", "content": "final", "filesize": 4760821, "license": "other", "mime_type": "application/pdf", "url": "/16640/1/Caltech_Thesis_final.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Quantum Gibbs Sampling", "author": [ { "family_name": "Chen", "given_name": "Chi-Fang", "orcid": "0000-0001-5589-7896", "clpid": "Chen-Chi-Fang" } ], "thesis_advisor": [ { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Tropp", "given_name": "Joel A.", "orcid": "0000-0003-1024-1791", "clpid": "Tropp-J-A" }, { "family_name": "Brandao", "given_name": "Fernando", "orcid": "0000-0003-3866-9378", "clpid": "Brand\u00e3o-F-G-S-L" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Markov Chain Monte Carlo algorithms are indispensable in classical thermodynamic simulation, perhaps due to their mathematical simplicity, algorithmic efficiency, and physical origin. In particular, Glauber dynamics is a detailed-balanced continuous-time Markov chain that fixes the Gibbs distribution and also serves as a mathematically succinct model of classical thermalization. In this thesis, we proposed a quantum computation analog of Glauber dynamics that is exactly detailed balanced yet algorithmic efficient, inherits the locality of the target Hamiltonian, and resembles Davies'-like generators physically derived from a weak system-bath coupling. We hope our proposal will serve as a quantum algorithm for quantum thermodynamic simulation and a model of open system thermalization where a suitable construction has been lacking for noncommuting Hamiltonians.", "doi": "10.7907/dy0f-3216", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:17150", "collection": "thesis", "collection_id": "17150", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04112025-180844471", "primary_object_url": { "basename": "Christopher_Yang_Thesis-2.pdf", "content": "final", "filesize": 20240940, "license": "other", "mime_type": "application/pdf", "url": "/17150/1/Christopher_Yang_Thesis-2.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Dynamical Control of Many-Body Interactions in Driven Quantum Matter", "author": [ { "family_name": "Yang", "given_name": "Christopher Kai-Chen", "orcid": "0000-0002-9462-9074", "clpid": "Yang-Christopher-Kai-Chen" } ], "thesis_advisor": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "thesis_committee": [ { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Strongly driven Floquet systems have emerged as promising platforms for exotic non-equilibrium physics, but their instability to heating motivates practical questions about how Floquet engineering can be useful. Although drive-induced heating is often attributed to interactions, this thesis adopts a different perspective, identifying regimes where dissipative many-body dynamics can stabilize Floquet physics and define remarkable new drive-tunable properties. This principle enables highly tunable many-body steady states with minimal heating, leading to a novel regime where drive control over single-particle Floquet states can extend to many-body interactions. Our theoretical and experimental results in Parts II and III center around two themes. The first theme focuses on discovering controllable and stable many-body Floquet states. The second explores further into what the future holds--envisioning the prospects for unconventional Floquet physics with nontraditional driving fields and three-dimensional materials.
\r\n\r\nPart II of this thesis leverages kinematic constraints on low-dimensional many-body scattering as new principles for tuning and stabilizing Floquet phases. First, we predict that a circularly polarized laser can drive slow electrons of moir\u00e9 systems into a subsonic regime where they decouple from the intrinsic 2D acoustic phonons of the system. This \"slow-electron regime\" enables optical control over the steady-state occupation of topological Floquet states and the resulting anomalous Hall conductivity. Second, we present experimental transport signatures of steady Floquet physics in graphene irradiated by a continuous-wave laser. Our experiment, performed at 3-4 K lattice temperatures with lasers off-resonant to optical phonons, creates electron-phonon scattering bottlenecks that stabilize persistent low-temperature phases with light-induced longitudinal transport characteristics. The long-lived many-body phase represents the first experimental signatures of steady Floquet physics in a metallic solid.
\r\n\r\nPart III presents emerging opportunities for many-body Floquet engineering beyond traditional optically-driven, low-dimensional materials. We first explore beyond-optical driving fields, revealing the emergence of quantized charge transport in 1D systems driven by coherent phonons. Incoherent phonons relax electrons into a topological spatiotemporal Floquet state with quantized group velocity set by the coherent phonon, realizing topological charge pumping in a highly non-adiabatic setting. Finally, we address the topological effects of time-periodic drives beyond low-dimensional systems, revealing that THz-frequency, circularly polarized light can induce topological chiral plasmons in Weyl semimetals with band anisotropy, broken time-reversal symmetry, and broken inversion symmetry.
\r\n\r\nThe theoretical and experimental work in this thesis represent key progress towards realizing persistent Floquet physics for diverse applications in quantum device engineering.
", "doi": "10.7907/fh52-tw61", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:17216", "collection": "thesis", "collection_id": "17216", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05092025-211543101", "primary_object_url": { "basename": "Zongyuan_Wang_PhD_thesis_2025.pdf", "content": "final", "filesize": 16910661, "license": "other", "mime_type": "application/pdf", "url": "/17216/1/Zongyuan_Wang_PhD_thesis_2025.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Type-I Fractons -- Foliation in Non-Abelian Models", "author": [ { "family_name": "Wang", "given_name": "Zongyuan", "orcid": "0000-0003-0813-6247", "clpid": "Wang-Zongyuan" } ], "thesis_advisor": [ { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" } ], "thesis_committee": [ { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Yeh", "given_name": "Nai-Chang", "orcid": "0000-0002-1826-419X", "clpid": "Yeh-Nai-Chang" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In this thesis, we present recent contributions to the study of Type-I non-abelian fracton models, which led us to propose the notion of generalized foliated fracton orders that captures the universal properties of both abelian and non-abelian Type-I fracton models.
\r\n\r\nFracton models are known for their exotic properties such as point-like excitations with restricted mobilities and robust topological ground state degeneracy that grows sub-extensively with the system size. A multitude of Type-I fracton models whose excitations obey either abelian or non-abelian fusion rules have recently been constructed. Among them, a large number of the abelian fracton models have been shown to possess foliation structures, where models of different system sizes can be related through the addition / removal of an entire piece of topologically ordered system on a sub-dimensional manifold via the action of a finite-depth local unitary circuit. In this thesis, this is referred to as the original foliation renormalization group (RG) scheme, which leads us to the notion of original foliation fracton orders. The Ising cage-net model and other similar non-abelian models are closely related to these abelian models in terms of their excitation structures and coupled layers construction etc. However, it was not known whether their fracton orders can also be understood within the original foliation framework. We address this problem in this thesis.
\r\n \r\nIn Chapter 2, we show that the Ising cage-net model does not fit into the original definition of foliated fracton orders, by calculating its ground state degeneracy. We realize that there exists naturally a more general way to define foliation -- the generalized foliation scheme (Chapter 3). The Ising cage-net and other similar non-abelian fracton models are foliated according to this generalized scheme. In the generalized foliation scheme, the RG transformation is defined by, from the excitation perspective, the condensation of planons / gauging subsystem symmetries. In terms of quantum circuits, this RG transformation is equivalent to a sequential linear-depth circuit that acts near a sub-dimensional manifold. With this definition, we can study phase relation of the Ising cage-net with other known fracton models. In Chapter 4, via gauging composite subsystem symmetries, we further show that the Ising cage-net belongs to the same generalized foliated fracton phases as the prototypical X-cube model. Furthermore, gauging composite subsystem symmetries opens up a new route to constructing non-abelian fracton models hosting exotic non-abelian fractons. An example is the tri-Ising-fracton model (Sec. 4.5).
", "doi": "10.7907/2x8m-j581", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:16461", "collection": "thesis", "collection_id": "16461", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06012024-162517388", "primary_object_url": { "basename": "Kaifu_Hiroki_2024.pdf", "content": "final", "filesize": 9564382, "license": "other", "mime_type": "application/pdf", "url": "/16461/1/Kaifu_Hiroki_2024.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Structural and Dynamical Correlations Linked to Smaller Thermal Resistance at a Classical Liquid/Solid Interface", "author": [ { "family_name": "Kaifu", "given_name": "Hiroki", "orcid": "0009-0003-2507-6810", "clpid": "Kaifu-Hiroki" } ], "thesis_advisor": [ { "family_name": "Troian", "given_name": "Sandra M.", "orcid": "0000-0003-1224-6377", "clpid": "Troian-S-M" } ], "thesis_committee": [ { "family_name": "Schwab", "given_name": "Keith C.", "orcid": "0000-0001-8216-4815", "clpid": "Schwab-K-C" }, { "family_name": "Troian", "given_name": "Sandra M.", "orcid": "0000-0003-1224-6377", "clpid": "Troian-S-M" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Porter", "given_name": "Frank C.", "orcid": "0000-0003-1948-8889", "clpid": "Porter-F-C" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Ever more powerful and densely packed chips for applications like cryptocurrency mining and artificial intelligence generate such enormous heat fluxes that designers are pivoting from gas to liquid cooling to forestall damage from thermal runaway. Even with optimal flow patterns however, the intrinsic thermal boundary resistance at the liquid/solid (L/S) interface poses an additional source of thermal impedance. There is a lingering misconception in the field that the higher the liquid contact density, the more frequent the L/S collision rate and the smaller the thermal slip length. Here we present an insightful counterexample based on non-equilibrium molecular dynamics simulations of a classical liquid confined between different facets of a face centered cubic crystal held at different temperature. We have conducted a comprehensive study to quantify thermal exchange and propagation across the interface by varying the L/S interaction energy, L/S repulsive distance, facet orientation, thermal flux and local temperature with particular emphasis on the properties of the liquid contact layer (i.e., liquid monolayer adjacent to the solid surface). Numerous static and dynamic quantities characterizing the contact layer reveal the ways in which long range order, anisotropy of the L/S potential and correlated motion act to reduce the thermal slip length. Systems with the smallest thermal slip length exhibit two distinct features: 2D caged motion with string-like alignment of liquid particles unlike that observed in glassy systems and larger non-ergodicity parameter but shorter, not longer, caging times.
\r\n\r\nThese simulations have revealed two master curves which help unify the various influences at play. The first relation directly links the thermal slip length to the temperature modified 2D static structure factor representing long-range order in the contact layer. The second relation directly links the thermal slip length to the temperature modified dominant frequencies of the first solid and liquid layer as extracted from the density of states. These correlations, which represent power law dependencies, offer a new paradigm for the design of L/S interfaces to maximize thermal exchange across a classical L/S interface.
", "doi": "10.7907/4z6h-v265", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:16379", "collection": "thesis", "collection_id": "16379", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05112024-185918688", "primary_object_url": { "basename": "Chang_Cyuan-Han_2024.pdf", "content": "final", "filesize": 3137852, "license": "other", "mime_type": "application/pdf", "url": "/16379/1/Chang_Cyuan-Han_2024.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Energy Correlators, Dispersive Sum Rules, and Modular Bootstrap in Conformal Field Theories", "author": [ { "family_name": "Chang", "given_name": "Cyuan-Han", "orcid": "0000-0002-7133-3553", "clpid": "Chang-Cyuan-Han" } ], "thesis_advisor": [ { "family_name": "Simmons-Duffin", "given_name": "David", "orcid": "0000-0002-2937-9515", "clpid": "Simmons-Duffin-D" } ], "thesis_committee": [ { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Ooguri", "given_name": "Hirosi", "orcid": "0000-0001-6021-3778", "clpid": "Ooguri-H" }, { "family_name": "Simmons-Duffin", "given_name": "David", "orcid": "0000-0002-2937-9515", "clpid": "Simmons-Duffin-D" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "In this thesis, we study various observables and constraints in conformal field theories. First, we consider a product of two null-integrated operators on the same null plane and derive an operator product expansion in the direction transverse to the null plane. We then generalize to the case of three null-integrated operators, and study constraints from Lorentz symmetry. We generate a class of dispersive CFT sum rules using commutativity of null-integrated operators, and build a dictionary between the CFT sum rules and the flat space dispersion relations. Finally, we consider two-dimensional conformal field theories and derive a scalar crossing equation using modular invariance.", "doi": "10.7907/na45-ng05", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:15213", "collection": "thesis", "collection_id": "15213", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05262023-213514916", "primary_object_url": { "basename": "Main_ChaoJungLee_PhDThesis_2023_0526.pdf", "content": "final", "filesize": 3276887, "license": "other", "mime_type": "application/pdf", "url": "/15213/1/Main_ChaoJungLee_PhDThesis_2023_0526.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "The Effects of Disorder and Interaction in Metallic Systems", "author": [ { "family_name": "Lee", "given_name": "Chao-Jung", "orcid": "0000-0003-3339-1522", "clpid": "Lee-Chao-Jung" } ], "thesis_advisor": [ { "family_name": "Mulligan", "given_name": "Michael", "orcid": "0009-0001-8457-986X", "clpid": "Mulligan-Michael" } ], "thesis_committee": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Mulligan", "given_name": "Michael", "orcid": "0009-0001-8457-986X", "clpid": "Mulligan-Michael" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Metallic states in two-dimensional quantum matter have a long history and pose extremely challenging problems. A generic metallic state is described by a gapless system with a finite density of particles, along with disorders and interactions. Such correlated many-body systems are usually difficult to study, both analytically and numerically. In this thesis, we are dedicated to certain simplified cases which enable us to study via analytical approaches. Firstly, we study the effects of quenched disorder and a dissipative Coulomb interaction in the Dirac composite fermion theory describing the quantum phase transition of integer quantum Hall plateau and magnetic-field tuned 2D supercondutor\r\nThe renormalization group study is presented, by considering the quantum effect of disorder and gauge fluctuation. Secondly, we present a study of integer quantum Hall plateau transition using a mean-field theory of composite fermions with a gyromagnetic ratio equal to two. We investigate the stability problem in terms of semi-classical approach and derive the corresponding nonlinear sigma model. Thirdly, we study a single 2D Dirac fermion at finite density, subjected to a quenched random magnetic field. The low-energy theory can be mapped onto an infinite collection of 1D chiral fermions coupled by a random vector potential matrix. The theory is exactly solvable, and the electrical response is computed non-perturbatively. Lastly, we shift our focus to a disorder-free system formed by a collection of 1D wires. We provide an example of an Ersatz Fermi liquid by deforming the chiral Wess-Zumino-Witten model with level k greater than unity.", "doi": "10.7907/p4b6-y780", "publication_date": "2023", "thesis_type": "phd", "thesis_year": "2023" }, { "id": "thesis:15183", "collection": "thesis", "collection_id": "15183", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05172023-003322589", "type": "thesis", "title": "Quantum States: With a View Toward Homological Algebra", "author": [ { "family_name": "Yang", "given_name": "Bowen", "orcid": "0000-0003-4778-831X", "clpid": "Yang-Bowen" } ], "thesis_advisor": [ { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" } ], "thesis_committee": [ { "family_name": "Marcolli", "given_name": "Matilde", "orcid": "0000-0002-2045-2907", "clpid": "Marcolli-M" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The thesis comprises three papers covering different topics in quantum many-body physics. The first paper examines translationally invariant Pauli stabilizer codes, introducing invariants called charge modules and discussing their properties. The second paper explores invertible (G-invariant) states of 1D bosonic quantum lattice systems (or spin chains), demonstrating a full classification using group cohomology. The third paper analyzes the relation between ordinary correlators and Kubo's canonical correlators for thermal states of systems with short-range interactions. Overall, the thesis highlights the power of mathematics, especially homological methods, in understanding quantum states.
", "doi": "10.7907/fm81-v416", "publication_date": "2023", "thesis_type": "phd", "thesis_year": "2023" }, { "id": "thesis:14645", "collection": "thesis", "collection_id": "14645", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05272022-220331463", "primary_object_url": { "basename": "Wilbur_Shirley_Thesis.pdf", "content": "final", "filesize": 26187118, "license": "other", "mime_type": "application/pdf", "url": "/14645/1/Wilbur_Shirley_Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Structure of Entanglement in Fracton Phases of Matter", "author": [ { "family_name": "Shirley", "given_name": "Wilbur Eric", "orcid": "0000-0002-4970-1460", "clpid": "Shirley-Wilbur-Eric" } ], "thesis_advisor": [ { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis discusses recent contributions to the theory of gapped fracton phases of matter, utilizing exactly solvable Hamiltonian models as the primary tool of study. A large component of the work revolves around the notion of a foliation structure, which is a defining feature of the long-range entanglement in certain gapped fracton states. We introduce this concept, identify its presence in a handful of prominent fracton models, and explore its consequences in terms of entanglement entropy and fractional excitations. A second major theme of the thesis is the characterization of gapped fracton states via emergent gauge theories based on discrete subsystem symmetries. We introduce a variety of novel fractonic gauge theories including twisted and fermionic variants, identify their emergence in a bevy of well-known models, and classify them with the use of novel topological invariants. We also establish a link between subsystem symmetry and entanglement renormalization group flow in fractal spin liquids.
", "doi": "10.7907/7b2c-2e06", "publication_date": "2022", "thesis_type": "phd", "thesis_year": "2022" }, { "id": "thesis:14144", "collection": "thesis", "collection_id": "14144", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05112021-235754667", "type": "thesis", "title": "Reducing Computational Costs for Many-Body Physics Problems", "author": [ { "family_name": "Ye", "given_name": "Erika", "orcid": "0000-0001-9694-568X", "clpid": "Ye-Erika" } ], "thesis_advisor": [ { "family_name": "Chan", "given_name": "Garnet K.", "orcid": "0000-0001-8009-6038", "clpid": "Chan-Garnet-K-L" }, { "family_name": "Minnich", "given_name": "Austin J.", "orcid": "0000-0002-9671-9540", "clpid": "Minnich-A-J" } ], "thesis_committee": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Refael", "given_name": "Gil", "clpid": "Refael-G" }, { "family_name": "Chan", "given_name": "Garnet K.", "orcid": "0000-0001-8009-6038", "clpid": "Chan-Garnet-K-L" }, { "family_name": "Minnich", "given_name": "Austin J.", "orcid": "0000-0002-9671-9540", "clpid": "Minnich-A-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Three different computational physics problems are discussed. The first project is solving the semi-classical Boltzmann transport equation (BTE) to compute the thermal conductivity of 1-D superlattices. We consider various spectral scattering models at each interface. This computation requires the inversion of a matrix whose size scales with the number of points used in the discretization of the Brillouin zone. We use spatial symmetries to reduce the size of data points and make the computation manageable. The other two projects involve quantum systems. Simulating quantum systems can potentially require exponential resources because of the exponential scaling of Hilbert space with system size. However, it has been observed that many physical systems, which typically exhibit locality in space or time, require much fewer resources to accurately simulate within some small error tolerance. The second project in the thesis is a two-step factorization of the electronic structure Hamiltonian that allows for efficient implementation on a quantum computer and also systematic truncation of small contributions. By using truncations that only incur errors below chemical accuracy, one is able to reduce the number of terms in the Hamiltonian from O(N\u2074) to O(N\u00b3), where N is the number of molecular orbitals in the system. The third project is a tensor network algorithm based on the concept of influence functionals (IFs) to compute long-time dynamics of single-site observables. IFs are high-dimensional objects that describe the influence of the bath on the dynamics of the subsystem of interest over all times, and we are interested in their low-rank approximations. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap, and find that the IFs can be efficiently computed and represented using tensor network methods. Consistent with physical intuition, the correlations in the IFs appear to decrease with increased bath sizes, suggesting that the low-rank nature of the IF is due to nontrivial cancellations in the bath.
", "doi": "10.7907/xpvv-ar02", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:14210", "collection": "thesis", "collection_id": "14210", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05312021-191637587", "primary_object_url": { "basename": "Thesis.pdf", "content": "final", "filesize": 5790355, "license": "other", "mime_type": "application/pdf", "url": "/14210/2/Thesis.pdf", "version": "v7.0.0" }, "type": "thesis", "title": "Exciton Dynamics Studies from First-Principles Calculations: Radiative Recombination, Exciton-Phonon Interactions, and Ultrafast Exciton Relaxation", "author": [ { "family_name": "Chen", "given_name": "Hsiao-Yi", "orcid": "000-0003-1962-5767", "clpid": "Chen-Hsiao-Yi" } ], "thesis_advisor": [ { "family_name": "Bernardi", "given_name": "Marco", "orcid": "0000-0001-7289-9666", "clpid": "Bernardi-Marco" } ], "thesis_committee": [ { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Yeh", "given_name": "Nai-Chang", "orcid": "0000-0002-1826-419X", "clpid": "Yeh-Nai-Chang" }, { "family_name": "Bernardi", "given_name": "Marco", "orcid": "0000-0001-7289-9666", "clpid": "Bernardi-Marco" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Excitons are bound electron-hole pairs that dominate the optical response of semi-conductors and insulators, especially in nanoscale and wide bandgap materials where the Coulomb interaction is weakly screened. Excitons can enhance light-matter coupling at certain wavelengths, thus making their host materials candidates for optoelectronic, photovoltaic, and quantum technology devices. For instance, two-dimensional transition metal dichalcogenides have a large and tunable optical response and hold promise for next-generation ultrathin light-emitting diodes. It is remarkable that exciton properties such as the binding energy and radiative lifetime can vary by orders of magnitude in different materials and can be further tuned by material properties like defects and lattice vibrations. Therefore, quantitative studies of exciton interactions and dynamics can advance understanding of the optical response of complex materials and play a role in the design of future devices. Among theoretical studies, numerical approaches based on density functional theory (DFT) can quantitatively address the electronic structure in real materials and their response to external perturbations, enabling accurate calculations of the conductivity and dielectric properties. These first-principle methods, which employ numerical quantum mechanics and use only the atomic structure of the material as input (making no use of empirical parameters) have revolutionized studies of materials and condensed matter physics. Over the last few years, first-principles methods for studies of excitons have focused on the GW-Bathe-Salpeter equation (GW-BSE) method to compute exciton energies and optical absorption spectra. However, going beyond calculations of exciton energetics to address the exciton dynamical processes remains challenging and is an exciting new frontier of first-principles studies.
\r\n\r\nThis thesis develops theory and novel numerical approaches to study exciton radiative and nonradiative interactions from first-principles. For the radiative processes, we demonstrate a systematic derivation of exciton radiative lifetimes in materials ranging from bulk to nanostructures and molecules. The results correctly reproduce the observed power-law temperature dependence of the radiative lifetimes. To benchmark our calculations, we study exciton radiative lifetimes in gas-phase molecules, obtaining excellent agreement between theory and experiment. Our framework is then applied in three different studies. First, we extend the radiative lifetime formula to account for the dependence on light polarization and valley occupation and investigate exciton recombination in two-dimensional transition metal dichalcogenides (2D-TMDs). We show that excitons emit light anisotropically upon recombination when they are in any quantum superposition state of the K and K' inequivalent valleys. When averaged over the emission angle and exciton momentum, our new treatment recovers the temperature-dependent radiative lifetimes derived in early literature. Second, we use the exciton energy and radiative lifetimes to identify the atomic structure of the defects in monolayer hexagonal boron nitride (h-BN). In the study, we narrow down the potential structures to nine candidates and identify the highest-likelihood structure as the VNNB defect, consisting of a nitrogen vacancy plus a carbon replacing boron in h-BN. Finally, we generalize the discussion of isotropic bulk system to accurately compute the exciton radiative lifetimes in bulk uniaxial crystals, focusing on wurtzite GaN. Our computed radiative lifetimes are in very good agreement with experiments at low temperature. We show that taking into account excitonic effect and spin-orbit coupling (to include the exciton fine structure) is essential for computing accurate radiative lifetimes. A model for exciton dissociation into free carriers allows us to compute the radiative lifetimes up to room temperature.
\r\n\r\nIn the study of exciton non-radiative process, we focus on the exciton-phonon (ex-ph)interaction, which plays an important role to understand the dynamics of excitons in materials. We establish and implement a first-principle formalism to compute the ex-ph coupling constants by combining the electron-phonon couplings and the exciton wavefunctions from the GW-BSE approach. Using the computed ex-ph coupling matrix elements, we calculate the ex-ph relaxation times as a function of exciton energy, momentum, temperature, and phonon mode in bulk h-BN. Our calculations reveal the dominant ex-ph coupling with the longitudinal optical (LO) mode and identify the threshold for LO phonon emission with an associated \u223c15 fs LO emission characteristic time. In addition, we derive the phonon-assisted photoluminescence(PL) from the ex-ph interaction and correctly reproduce the PL spectrum observed in h-BN at both 8 K and 100 K. Based on our successful study of ex-ph interactions in bulk h-BN, we extend the discussion to materials with strong spin-orbit coupling. We investigate the bright exciton linewidth broadening and PL in monolayer WSe2. The numerical results show an increase of linewidth by 20 meV from 0 K to 250 K as observed in early experiments and identify the main PL peak as a consequence of LA phonon emission while the side band is due to optical phonons. Lastly, we present results from a joint theory-experiment study of the ultrafast exciton dynamics in WSe2. We develop a Boltzmann equation for excitons and employ it to model ultrafast exciton relaxation due to ex-ph processes. The simulation and experiment both show a ~70 fs time delay for the electron intervalley scattering from the K- to the Q-valley due to exciton dynamical effects. We also develop accurate simulations of time-domain angle-resolved photoemission (ARPES) experiments, which are becoming a powerful experimental probe of exciton dynamics in condensed matter. In summary, this thesis work paves the way to quantitative studies of exciton radiative and non-radiative processes, as well as exciton ultrafast dynamics, and quantitative modeling of pump-probe experiments in materials with strongly bound excitons.
", "doi": "10.7907/4edg-jw48", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:14145", "collection": "thesis", "collection_id": "14145", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05122021-000037101", "type": "thesis", "title": "New Tensor Network Methods and Studies of Criticality in Low-Dimensional Quantum Systems", "author": [ { "family_name": "Roberts", "given_name": "Brenden Carlisle", "orcid": "0000-0002-3107-1878", "clpid": "Roberts-Brenden-Carlisle" } ], "thesis_advisor": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "thesis_committee": [ { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Simmons-Duffin", "given_name": "David", "orcid": "0000-0002-2937-9515", "clpid": "Simmons-Duffin-D" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Several investigations are presented around the general topic of the ground state and low-energy behavior of models for many-body quantum physics in one dimension (1d). We develop a novel numerical method for the ground and low-energy sectors of local Hamiltonians in 1d which is based on proofs from quantum information theory. This method, the rigorous renormalization group (RRG), enjoys the benefits of explicit global information from the Hamiltonian in its local step, allowing it to avoid spurious convergence in systems with challenging energy landscapes. We apply RRG to the random XYZ spin chain in an unbiased numerical study evaluating infinite-randomness fixed point physics and continuously varying critical exponents in the ground state, finding evidence for both. In a related effective model with correlations preventing the exact solution of the strong-disorder renormalization group equations, we use the framework of random walks to rigorously establish continuously varying critical exponents. We also perform detailed studies of deconfined quantum critical points (DQCP) in 1d, providing strong evidence for phase transitions which display similar phenomenology to the canonical examples in 2d. A family of DQCP phase transitions in 1d is exhibited which appears to controlled by complex fixed points corresponding to a walking scenario for renormalization group flows.", "doi": "10.7907/vhwq-gz88", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:13859", "collection": "thesis", "collection_id": "13859", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:08272020-235955490", "primary_object_url": { "basename": "Caltech_Thesis_Minyoung_You.pdf", "content": "final", "filesize": 730006, "license": "other", "mime_type": "application/pdf", "url": "/13859/1/Caltech_Thesis_Minyoung_You.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Topological Phases of Matter: Classification, Stacking Law, and Relation to Topological Quantum Field Theory", "author": [ { "family_name": "You", "given_name": "Minyoung", "orcid": "0000-0002-8251-953X", "clpid": "You-Minyoung" } ], "thesis_advisor": [ { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" } ], "thesis_committee": [ { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Marcolli", "given_name": "Matilde", "orcid": "0000-0002-2045-2907", "clpid": "Marcolli-M" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We study aspects of gapped phases of matter, focusing on their classification, including the group law under stacking, and their relation to topological quantum field theories (TQFT). In one spatial dimension, it is well-known that Matrix Product States (MPS) efficiently approximate ground states of gapped systems; by showing that these states arise naturally in 1 + 1-dimensional lattice TQFT, which in turn are closely related to continuum TQFT, we provide a concrete connection between ground states of lattice systems and TQFT in 1 + 1 dimensions. We generalize this to systems with symmetries and fermions, and obtain a classification and group law for the stacking of 1 + 1-dimensional symmetry-protected topological phases. Further, we study the effect of turning on/off interactions for the classification: the phase classification of a given symmetry class of Hamiltonians can be different depending on whether we allow interactions or not, and in low dimensions we provide some concrete formulas relating the phases under the non-interacting classification and those under the interacting classification. Lastly, we study the phases of the 2 + 1-dimensional topological superconductor, and show that for all 16 phases braiding statistics of vortices, which determine the underlying TQFT, can be obtained by stacking layers of the basic p + ip superconductor.
", "doi": "10.7907/4xq7-gh61", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:13768", "collection": "thesis", "collection_id": "13768", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06022020-110730808", "type": "thesis", "title": "Development of Tools for Probing Order in Single Crystals Using Electron and Photon Spectroscopy", "author": [ { "family_name": "Deshpande", "given_name": "Tejas Makarand", "orcid": "0000-0003-0326-1372", "clpid": "Deshpande-Tejas-Makarand" } ], "thesis_advisor": [ { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" } ], "thesis_committee": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Discovering novel quantum phases of matter\u2013from emergent behavior of strongly-correlated electrons in solid-state systems to superfluidity in quantum degenerate liquids\u2013has been a cornerstone of condensed matter physics for many decades. In the most recent decades, however, the discovery of topological phases has emphasized the importance of symmetry, in addition to the conventional paradigm of symmetry breaking, in the definition of the order parameter, \u03a8, and hence the quantum phase it represents. Naturally, novel experimental tools, capable of coupling to said order parameter, directly or indirectly, are required to discover conventionally elusive quantum phases. In this thesis, I will discuss experimental techniques, using both photon and electron spectroscopy, to study exotic electronic phases in single crystals. The thesis will be divided into two unequal parts: (a) the development of a high-energy-resolution sub-Kelvin angle-resolved photoemission spectroscopy apparatus to study 3D time-reversal invariant topological superconductors, and (b) the experiments exploiting the non-linear and time-resolved aspects of femtosecond lasers to study a broad class of many-body systems.
", "doi": "10.7907/tt7b-fm83", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:13788", "collection": "thesis", "collection_id": "13788", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06082020-083409184", "primary_object_url": { "basename": "Chen_Yu_An_2020_thesis.pdf", "content": "final", "filesize": 1945057, "license": "other", "mime_type": "application/pdf", "url": "/13788/8/Chen_Yu_An_2020_thesis.pdf", "version": "v6.0.0" }, "type": "thesis", "title": "Exact Bosonization in All Dimensions: the Duality Between Fermionic and Bosonic Phases of Matter", "author": [ { "family_name": "Chen", "given_name": "Yu-An", "orcid": "0000-0002-8810-9355", "clpid": "Chen-Yu-An" } ], "thesis_advisor": [ { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" } ], "thesis_committee": [ { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "We describe an n-dimensional (n\u22652) analog of the Jordan-Wigner transformation, which maps an arbitrary fermionic system to Pauli matrices while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization gives a duality between any fermionic system in arbitrary n spatial dimensions and a new class of (n-1)-form Z\u2082 gauge theories in n dimensions with a modified Gauss\u2019s law. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model, and 3d bosonization, including a solvable Z\u2082 lattice gauge theory with Dirac cones in the spectrum. This bosonization formalism has an explicit dependence on the second Stiefel-Whitney class and a choice of spin structure on the manifold, a key feature for defining fermions. A new formula for Stiefel-Whitney homology classes on lattices is derived. We also derive the Euclidean actions for the corresponding lattice gauge theories from the bosonization. The topological actions contain Chern-Simons terms for (2+1)D or Steenrod Square terms for general dimensions. Finally, we apply the bosonization to construct various bosonic or fermionic symmetry-protectedtopological (SPT) phases. It has been shown that supercohomology fermionic SPT phases are dual to bosonic higher-group SPT phases.", "doi": "10.7907/593v-5r52", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:13705", "collection": "thesis", "collection_id": "13705", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05142020-114820618", "type": "thesis", "title": "Enriching Majorana Zero Modes", "author": [ { "family_name": "Chew", "given_name": "Aaron", "orcid": "0000-0003-0448-6215", "clpid": "Chew-Aaron" } ], "thesis_advisor": [ { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" } ], "thesis_committee": [ { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Nadj-Perge", "given_name": "Stevan", "orcid": "0000-0002-2394-9070", "clpid": "Nadj-Perge-S" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "My various projects in graduate school have centered around a common theme: harnessing relatively well-understood phases of matter and combining them to create exotic physics. They also involve Majoranas, or more accurately, defects that bind Majorana zero modes and are the centerpiece for topological quantum computation. We exploit and enrich this Majorana zero mode by employing topological superconductors, time crystals, and quantum dots and combining them together. Our first project involved joining Majorana nanowires and quantum dots to simulate the SYK model, a zero-dimensional strongly interacting phase with connections to black holes and holography. We follow by explaining how to combine spontaneous symmetry-breaking with topological superconductivity to recover parafermion physics in one dimension. We explain an exact mapping that relates fermions to parafermions, illustrating a deep connection between different one-dimensional phases of matter. We finally show that enhancing the topological superconductor with a time crystal, a phase of matter that spontaneously breaks time-translation symmetry, creates an anomalous zero mode that displays 4Tperiodicity in the Floquet drive. By combining these different phases in judicious ways we achieve exotic physics unattainable by the constituent parts. Our work thus illustrates profitable directions for harnessing Majorana zero modes to study the physics of exotic matter.
", "doi": "10.7907/91q9-9606", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:11558", "collection": "thesis", "collection_id": "11558", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05292019-112014488", "primary_object_url": { "basename": "white_christopher_2019.pdf", "content": "final", "filesize": 5794816, "license": "other", "mime_type": "application/pdf", "url": "/11558/1/white_christopher_2019.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Numerical Methods for Many-Body Quantum Dynamics", "author": [ { "family_name": "White", "given_name": "Christopher David", "orcid": "0000-0002-8372-2492", "clpid": "White-Christopher-David" } ], "thesis_advisor": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "thesis_committee": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Mong", "given_name": "Roger S.", "orcid": "0009-0000-7182-5681", "clpid": "Mong-Roger-S" }, { "family_name": "Endres", "given_name": "Manuel A.", "orcid": "0000-0002-4461-224X", "clpid": "Endres-M" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "This thesis describes two studies of the dynamics of many-body quantum systems with extensive numerical support.
\r\n\r\nIn Part I we first give a new algorithm for simulating the dynamics of one-dimensional systems that thermalize (that is, come to local thermal equilibrium). The core of this algorithm is a new truncation for matrix product operators, which reproduces local properties faithfully without reproducing non-local properties (e.g. the information required for OTOCs). To the extent that the dynamics depends only on local operators, timesteps interleaved with this truncation will reproduce that dynamics.
\r\n\r\nWe then apply this to algorithm to Floquet systems: first to clean, non-integrable systems with a high-frequency drive, where we find that the system is well-described by a natural diffusive phenomenology; and then to disordered systems with low-frequency drive, which display diffusion \u2014 not subdiffusion \u2014 at appreciable disorder strengths.
\r\n\r\nIn Part II, we study the utility of many-body localization as a medium for a thermodynamic engine. We first construct a small (\"mesoscale\") engine that gives work at high efficiency in the adiabatic limit, and show that thanks to the slow spread of information in many body localized systems, these mesoscale engines can be chained together without specially engineered insulation. Our construction takes advantage of precisely the fact that MBL systems do not thermalize. We then show that these engines still have high efficiency when run at finite speed, and we compare to competitor engines.
\r\n", "doi": "10.7907/VC0P-3K15", "publication_date": "2019", "thesis_type": "phd", "thesis_year": "2019" }, { "id": "thesis:11588", "collection": "thesis", "collection_id": "11588", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05312019-162611521", "primary_object_url": { "basename": "Turzillo-THESIS-final.pdf", "content": "final", "filesize": 1553691, "license": "other", "mime_type": "application/pdf", "url": "/11588/1/Turzillo-THESIS-final.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Short-Range Entangled Phases of Fermions", "author": [ { "family_name": "Turzillo", "given_name": "Alexander Michael", "orcid": "0000-0003-4293-4293", "clpid": "Turzillo-Alexander-Michael" } ], "thesis_advisor": [ { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" } ], "thesis_committee": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Marcolli", "given_name": "Matilde", "orcid": "0000-0002-2045-2907", "clpid": "Marcolli-M" }, { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis is an attempt to understand the physics of short-range entangled phases of fermions through several related approaches. The first angle is topological quantum field theory. We discuss the classification of interacting fermionic short-range entangled phases by spin cobordism and give an algebraic characterization of unoriented equivariant bosonic topological quantum field theories in one spatial dimension. A second tool is tensor network representation. We develop the formalism of fermionic matrix product states and use it to derive the stacking group law for one dimensional symmetry-enriched fermionic short-range entangled phases. We also study its relationship with state sum constructions of topological quantum field theories and develop a state sum construction for pin-minus theories in one spatial dimension. The third approach is topological band theory. We classify free fermionic phases enriched by a unitary symmetry in any dimension and determine the map into the interacting classification.", "doi": "10.7907/3JR4-8G12", "publication_date": "2019", "thesis_type": "phd", "thesis_year": "2019" }, { "id": "thesis:11538", "collection": "thesis", "collection_id": "11538", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05232019-192004916", "primary_object_url": { "basename": "Lin__Cheng_Ju__2019.pdf", "content": "final", "filesize": 18638108, "license": "other", "mime_type": "application/pdf", "url": "/11538/1/Lin__Cheng_Ju__2019.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Surviving Quantum Chaos: Weak Thermalization, Prethermalization and Quantum Many-Body Scar States", "author": [ { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" } ], "thesis_advisor": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "thesis_committee": [ { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "Quantum chaos and the eigenstate thermalization hypothesis are based on the assumption of the validity of random matrix theory description on the spectrum and eigenstates. They provide the foundation and descriptions for the typical dynamics and thermalization in generic closed quantum systems. In this thesis, we investigate situations where the systems show atypical dynamics or anomalous thermalization, conflicting with the usual expectations from quantum chaos and eigenstate thermalization hypothesis.\r\nWe first examine weak thermalization in a nonintegrable spin chain. The system shows long-lived strong oscillations and relaxes to the thermal equilibrium weakly. We identify the dynamics describable by quasiparticles and recognize the oscillation frequency to be the quasiparticle mass gap. We also estimate the damping time for the oscillations.\r\nNext, we study prethermalization, a phenomenon where a system relaxes to an intermediate almost-equilibrium stage before reaching the true thermal equilibrium. We study a nonintegrable spin chain in the strong coupling limit, where an almost-conserved quantity emerges and gives rise to the prethermalization.\r\nWe also study a newly proposed diagnostic for quantum chaos: out-of-time-ordered correlators. Contrasting to the chaotic systems, we inspect their behaviors in various noninteracting integrable models.\r\nFinally, we dig into the quantum many-body scar states in the PXP model which describes a Rydberg atom chain. These special states do not satisfy the random matrix theory description nor the eigenstate thermalization hypothesis, therefore defying quantum chaos.", "doi": "10.7907/DKYP-PH92", "publication_date": "2019", "thesis_type": "phd", "thesis_year": "2019" }, { "id": "thesis:11726", "collection": "thesis", "collection_id": "11726", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06082019-034706928", "primary_object_url": { "basename": "einav_tal_2019_thesis.pdf", "content": "final", "filesize": 40337719, "license": "other", "mime_type": "application/pdf", "url": "/11726/1/einav_tal_2019_thesis.pdf", "version": "v6.0.0" }, "type": "thesis", "title": "Taming the Molecular Dance: Harnessing Statistical Mechanics to Quantitatively Characterize Allosteric Systems", "author": [ { "family_name": "Einav", "given_name": "Tal", "orcid": "0000-0003-0777-1193", "clpid": "Einav-Tal" } ], "thesis_advisor": [ { "family_name": "Phillips", "given_name": "Robert B.", "orcid": "0000-0003-3082-2809", "clpid": "Phillips-R" } ], "thesis_committee": [ { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Phillips", "given_name": "Robert B.", "orcid": "0000-0003-3082-2809", "clpid": "Phillips-R" }, { "family_name": "Bois", "given_name": "Justin S.", "orcid": "0000-0001-7137-8746", "clpid": "Bois-J-S" }, { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The pace of biological research continues to grow at a staggering pace as high-throughput experimental techniques rapidly increase our ability to sequence DNA, quantify cell behavior, and image molecules of all types within the cellular milieu. Given this surge in experimental prowess, the time is ripe to examine how well our conceptual cartoons of biological phenomena can not only recapitulate the data but also successfully predict the outcomes of future experiments.
\r\n\r\nOne of the fundamental challenges in biology is that the space of possible molecules is overwhelmingly large. The number of variants of a moderately-sized protein (20^300) is larger than the number of atoms in the universe, as is the space of possible bacterial genomes, protein interaction networks, and effector functions; progress in any of these fronts requires a theory-experiment dialogue that can extrapolate our small drop of data to explain large swaths of parameter space.
\r\n\r\nMy thesis strives towards this goal by analyzing a number of central molecular players in biology including enzymes (biological catalysts that accelerate chemical reactions), transcription factors (proteins that bind to DNA and regulate its expression), and ion channels (signaling proteins that regulate ion transport). I develop a quantitative description in each context by harnessing the statistical mechanical Monod-Wyman-Changeux model of allostery which coarse-grains the behavior of a multi-state system into two effective states, demonstrating that these seemingly diverse molecules are all governed by the same fundamental equation.
\r\n\r\nWrit large, there are two overarching goals encompassed by these projects. The first is to translate our biological knowledge into concrete physical models, enabling us to quantitatively describe how the key molecular components in each system interact to carry out their function. The second goal is to analyze how mutations can be mapped into the fundamental biophysical parameters governing each system. In my opinion, predicting the effects of mutations remains one of the great unsolved problems in biology, and it has been incredibly exciting to make progress on this front.
\r\n\r\nLooking back at my amazing graduate school experience, one of the most surprising aspects of my PhD was how closely each of my projects revolved around experiments. I entered graduate school as a theoretical physicist expecting to work on esoteric mathematical models, yet the direct connection with data provided a window into the exhilarating world of biology. While I have never physically manipulated these biological systems in the lab, my models allow me to push and prod and examine their behavior from the most mundane to the utterly extreme limits. Through modeling, I test our assumptions of how these systems work and tease out insights into their underlying biophysical mechanism. Most importantly, these models enable me to harness the incredible wealth of hard-won data to weave a few more threads of understanding into our tapestry of how these incredible living systems operate.
", "doi": "10.7907/S4CV-T162", "publication_date": "2019", "thesis_type": "phd", "thesis_year": "2019" }, { "id": "thesis:10982", "collection": "thesis", "collection_id": "10982", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05312018-132922155", "type": "thesis", "title": "Super Pivotal Categories, Fermion Condensation, and Fermionic Topological Phases", "author": [ { "family_name": "Aasen", "given_name": "David", "orcid": "0000-0002-6552-488X", "clpid": "Aasen-David" } ], "thesis_advisor": [ { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" } ], "thesis_committee": [ { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Chen", "given_name": "Xie", "orcid": "0000-0003-2215-2497", "clpid": "Chen-Xie" }, { "family_name": "Nadj-Perge", "given_name": "Stevan", "orcid": "0000-0002-2394-9070", "clpid": "Nadj-Perge-S" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_eng" } ], "abstract": "We describe a systematic way of producing fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain an emergent fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions, and condensing pairs of physical and emergent fermions. There are two distinct types of objects in fermionic theories, which we call “m-type” and “q-type” particles. The endomorphism algebras of q-type particles are complex Clifford algebras, and they have no analogues in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations in fermionic topological phases. We then prove a series of results relating data in condensed theories to data in their parent theories; for example, if C is a modular tensor category containing a fermion, then the tube category of the condensed theory satisfies Tube(C/ψ) ≅ C × C/ψ. We also study how modular transformations, fusion rules, and coherence relations are modified in the fermionic setting, prove a fermionic version of the Verlinde dimension formula, construct a commuting projector lattice Hamiltonian for fermionic theories, and write down a fermionic version of the Turaev-Viro-Barrett-Westbury state sum.
", "doi": "10.7907/P9A4-MH26", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10992", "collection": "thesis", "collection_id": "10992", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05312018-184631141", "primary_object_url": { "basename": "fishman_matthew_2018.pdf", "content": "updated", "filesize": 1341193, "license": "other", "mime_type": "application/pdf", "url": "/10992/28/fishman_matthew_2018.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Development of Tensor Network Algorithms for Studying Classical and Quantum Many-Body Systems", "author": [ { "family_name": "Fishman", "given_name": "Matthew Theodore", "clpid": "Fishman-Matthew-Theodore" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "White", "given_name": "Steven R.", "clpid": "White-S-R" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "White", "given_name": "Steven R.", "clpid": "White-S-R" }, { "family_name": "Chan", "given_name": "Garnet K.", "orcid": "0000-0001-8009-6038", "clpid": "Chan-G-K" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "The field of tensor networks, kicked off in 1992 by Steve White's invention of the spectacularly successful density matrix renormalization group (DMRG) algorithm, has exploded in popularity in recent years. Tensor networks are poised to play a role in helping us solve some of the greatest open physics problems of our time, such as understanding the nature of high-temperature superconductivity and illuminating a theory of quantum gravity. DMRG and extensions based on a class of variational states known as tensor network states have been indispensable tools in helping us understand both numerically and theoretically the properties of complicated classical and quantum many-body systems. However, practical challenges to these techniques still remain, and algorithmic developments are needed before tensor network algorithms can be applied to more physics problems. In this thesis we present a variety of recent advancements to tensor network algorithms.
\r\n\r\nFirst we describe a DMRG-like algorithm for noninteracting fermions. Noninteracting fermions, naturally being gapless and therefore having high levels of entanglement, are actually a challenging setting for standard DMRG algorithms, and we believe this new algorithm can help with tensor network calculations in that setting.
\r\n\r\nNext we explain a new algorithm called the variational uniform matrix product state (VUMPS) algorithm that is a DMRG-like algorithm that works directly in the thermodynamic limit, improving upon currently available MPS-based methods for studying infinite 1D and quasi-1D quantum many-body systems.
\r\n\r\nFinally, we describe a variety of improvements to algorithms for contracting 2D tensor networks, a common problem in tensor network algorithms, for example for studying 2D classical statistical mechanics problems and 2D quantum many-body problems with projected entangled pair states (PEPS). One is a new variant of the corner transfer matrix renormalization group (CTMRG) algorithm of Nishino and Okunishi that improves the numerical stability for contracting asymmetric two-dimensional tensor networks compared to the most commonly used method. Another is the application of the VUMPS algorithm to contracting 2D tensor networks. The last is a new alternative to CTMRG, where the tensors are solved for with eigenvalue equations instead of a power method, which we call the fixed point corner method (FPCM). We present results showing the transfer matrix VUMPS algorithm and FPCM significantly improve upon the convergence time of CTMRG. We expect these algorithms will play an important role in expanding the set of 2D classical and 2D quantum many-body problems that can be addressed with tensor networks.
", "doi": "10.7907/44s6-0q68", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:11019", "collection": "thesis", "collection_id": "11019", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06042018-162115007", "type": "thesis", "title": "The Effective Field Theory of Fermi Surfaces in the Vicinity of Van Hove Singularities", "author": [ { "family_name": "McKinney", "given_name": "Tristan James", "orcid": "0000-0003-2365-1810", "clpid": "McKinney-Tristan-James" } ], "thesis_advisor": [ { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" } ], "thesis_committee": [ { "family_name": "Kapustin", "given_name": "Anton N.", "orcid": "0000-0003-3903-5158", "clpid": "Kapustin-A" }, { "family_name": "Wise", "given_name": "Mark B.", "orcid": "0000-0002-9125-801X", "clpid": "Wise-M-B" }, { "family_name": "Spiropulu", "given_name": "Maria", "orcid": "0000-0001-8172-7081", "clpid": "Spiropulu-M" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "Walter Burke Institute for Theoretical Physics" }, { "literal": "div_pma" } ], "abstract": "The use of effective field theories to attack new and seemingly disparate problems has proliferated in the past several decades. In this thesis, we develop effective field theories for systems of fermionic quasiparticles possessing Fermi surfaces, with a particular focus on Fermi surfaces proximal to Van Hove singularities. Such systems are a fruitful source of complex and novel behavior in condensed matter physics. We begin with an overview of the renormalization group procedure at the heart of effective field theory by analyzing a simple example. We emphasize the concept that the RG relates the observables of one theory to those of another theory with precisely the same form but different numerical parameters. We also note the generality and extensibility of these concepts. We then apply this perspective to the study of quasiparticles with a round Fermi surface, employing the technique of binning the quasiparticle fields in momentum space to translate previous treatments into a more modern form. We next develop an effective field theory describing the excitations of modes around a Fermi surface with a Van Hove singularity. We resolve lingering questions about the presence of nonlocal interactions in similar models. We find a rich and complicated theory capable of describing deviations from typical Fermi liquid behavior that nonetheless displays some universal dependence on the interactions involving modes in the vicinity of the Van Hove point. We close with an analysis of the instabilities of this Van Hove effective field theory.
", "doi": "10.7907/8VWF-V806", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:11032", "collection": "thesis", "collection_id": "11032", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06062018-171256773", "type": "thesis", "title": "Thermalization in Periodically-Driven Interacting Quantum Systems", "author": [ { "family_name": "Seetharam", "given_name": "Karthik Iyengar", "orcid": "0000-0003-1928-8019", "clpid": "Seetharam-Karthik-Iyengar" } ], "thesis_advisor": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "thesis_committee": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_eng" } ], "abstract": "Periodically-driven (Floquet) quantum systems are ubiquitous in science and technology. For example, when a laser illuminates a material or an AC voltage is applied to a device, the system is well-described by a time-periodic Hamiltonian. In recent years, periodic driving has been proposed, not just as a tool to excite and probe devices, but actually as a mechanism of engineering new phases of matter, some of which have no equilibrium analog. However, with this promise comes a serious problem. Intuitively, if energy is injected into and distributed throughout a system, it is no surprise that it tends to heat up indefinitely to infinite temperature.
\r\n\r\nIn this thesis, we study the mechanisms of heating, i.e. the process of thermalization, in Floquet systems and propose methods to control them. Specifically, for non-interacting Floquet systems that are coupled to external bosonic and fermionic baths (e.g. laser-driven electrons in a semiconductor that interact with phonons and an external lead), we classify the relevant scattering processes that contribute to cooling/heating in the Floquet bands and suggest methods to suppress heating via bandwidth-restrictions on the baths. We find that is possible, with appropriate dissipative engineering, to stabilize a controlled incompressible nonequilibrium steady-state resembling a ground state - a state we term the \"Floquet insulator.\" We extend this analysis to include short-range interactions that contribute additional heating processes and show, under the same framework, that heating can be controlled with dissipation. In the process, we develop a simple effective model for the Floquet band densities that captures the essence of all the Floquet scattering processes and that is useful for ballparking experimentally-relevant estimates of heating. Next, we turn our attention to strongly-interacting closed Floquet systems and study how heating emerges through a proliferation of resonances. We find a novel integrable point governing the strong-interaction limit of the Floquet system and examine the breakdown of integrability via the proliferation of resonances. We observe two distinct scaling regimes, attributed to non-thermal and thermal behavior, and discover a power-law scaling of the crossover between them as a function of system size. The lingering ergodicity-breaking effects of the conserved quantities in the vicinity (in parameter space) of the integrable point at finite size is a phenomena we term \"near-integrability.\" These results suggest that small quantum systems, which are accessible currently in many platforms (e.g. trapped ions, cold atoms, superconducting devices), intrinsically host non-thermal states that one may be able to utilize to avoid heating. Furthermore, our results suggest a \"dual\" interpretation, in the thermodynamic limit, that a periodically-driven system exhibits prethermalization as a power-law in interaction strength.
", "doi": "10.7907/3G0V-TW52", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:9919", "collection": "thesis", "collection_id": "9919", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09082016-145215432", "primary_object_url": { "basename": "Nicolaou_Zachary_2017.pdf", "content": "final", "filesize": 21224420, "license": "other", "mime_type": "application/pdf", "url": "/9919/1/Nicolaou_Zachary_2017.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Symmetry and Variational Analyses of Fluid Interface Equations in the Thin Film Limit", "author": [ { "family_name": "Nicolaou", "given_name": "Zachary George", "orcid": "0000-0003-4542-4256", "clpid": "Nicolaou-Zachary-George" } ], "thesis_advisor": [ { "family_name": "Troian", "given_name": "Sandra M.", "orcid": "0000-0003-1224-6377", "clpid": "Troian-S-M" } ], "thesis_committee": [ { "family_name": "Troian", "given_name": "Sandra M.", "orcid": "0000-0003-1224-6377", "clpid": "Troian-S-M" }, { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Brady", "given_name": "John F.", "orcid": "0000-0001-5817-9128", "clpid": "Brady-J-F" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "This thesis concerns a class of nonlinear partial differential equations up to fourth order in spatial derivatives that models thin viscous films. In Chapter 1, we review the derivations of thin film equations from the fundamental transport equations. Section 1.1 contains the derivation for a thermocapillary driven film to familiarize the reader with the key long-wavelength approximation that has been successful in modeling a myriad of thin viscous films. In Section 1.2, we consider the coupling between a thin viscous layer and a much thicker fluid layer with much larger viscosity and conductivity and show how a novel, non-local thermocapillary thin film equation can be derived to model such a system. We then review the wider class of thin film equations in Section 1.3, note the important Cahn-Hilliard variational form of these equations, and demonstrate that classic mathematical results concerning the inverse problem of the calculus of variations permit an algorithmic procedure for discovering Lyapunov functionals. In Chapter 2, we review applications of symmetry methods to partial differential equations. Section 2.1 contains an original geometrical motivation for the study of self-similar reductions which draws an analogy with the fixed points of dynamical systems. In Section 2.2, we derive for the first time the full set of symmetries of the fully two-dimensional thin film equations. We then enumerate the possible symmetry reductions of the thin film equations, and discover several which have not been previously recognized. In Chapter 3, we consider rotationally invariant, steady droplet solutions and their stability. In Section 3.1, we derive stability criteria for thermocapillary-driven droplets, and show a novel correspondence between droplet stability, droplet volume, and droplet Lyapunov energy. We consider thin films under other forces in Section 3.2 and make new predictions about conditions under which such films develop into droplets, columns, or jets of fluid. In Chapter 4, we consider the scale invariant symmetry reductions of thin film equations. In Section 4.1 we describe the extraordinarily rich variety of such solutions in the spreading of a insoluble surfactant on a thin viscous film, identify previously unrecognized scale invariant solutions which are well-behaved at the origin, and demonstrate their relevance with finite element simulations. Lastly, in Section 4.2, we illustrate for capillary driven films some numerical solutions to the novel reductions we uncovered in Chapter 2. Each chapter concludes with a Notes section which summarizes the new results contained therein and relates them to the wider literature.", "doi": "10.7907/Z9R20ZBS", "publication_date": "2017", "thesis_type": "phd", "thesis_year": "2017" }, { "id": "thesis:10207", "collection": "thesis", "collection_id": "10207", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05252017-092503939", "primary_object_url": { "basename": "main.pdf", "content": "final", "filesize": 1104452, "license": "other", "mime_type": "application/pdf", "url": "/10207/1/main.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Mathematical Results on Quantum Many-Body Physics", "author": [ { "family_name": "Lemm", "given_name": "Marius Christopher", "orcid": "0000-0001-6459-8046", "clpid": "Lemm-Marius-Christopher" } ], "thesis_advisor": [ { "family_name": "Frank", "given_name": "Rupert L", "orcid": "0000-0001-7973-4688", "clpid": "Frank-R-L" } ], "thesis_committee": [ { "family_name": "Frank", "given_name": "Rupert L.", "orcid": "0000-0001-7973-4688", "clpid": "Frank-R-L" }, { "family_name": "Makarov", "given_name": "Nikolai G.", "clpid": "Makarov-N-G" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Simon", "given_name": "Barry M.", "orcid": "0000-0003-2561-8539", "clpid": "Simon-B" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The collective behavior exhibited by a large number of microscopic quantum particles is at the heart of some of the most striking phenomena in condensed matter physics such as Bose-Einstein condensation and superconductivity. Physicists and mathematicians have made great progress in understanding when and how these collective phenomena emerge through the interplay of particle statistics, particle interaction and the value of thermodynamic parameters like the temperature or the chemical potential. Due to the extreme complexity of realistic many-body systems, it is natural to introduce appropriate simplifications to render their analysis feasible. Three examples of such simplifications which have proven themselves as viable starting points for a fruitful and mathematically rigorous analysis of many-body systems are the following: (a) the study of integrable models; (b) the derivation of effective theories, valid on a macroscopic scale, from more fundamental microscopic theories under appropriate coarse-graining; and (c) the use of quantum information theory to understand general connections between correlation, entanglement and particle statistics.
\r\n\r\nIn this thesis, we present mathematically rigorous results that were obtained in these three directions. (1) We prove anomalous quantum many-body transport in XY quantum spin chains for certain choices of the external magnetic field. The anomalous transport is described via new kinds of anomalous Lieb-Robinson bounds, including one of power-law type. We note that the XY spin chain is integrable as it can be mapped to free fermions via the non-local Jordan-Wigner transformation. (2) We derive effective macroscopic theories of Ginzburg-Landau type from the microscopic BCS theory of superconductivity in certain circumstances. We study the case of a multi-component order parameter for translation-invariant systems and the condensation of fermion pairs at zero temperature in a domain with a hard boundary. (3) We use techniques from quantum information-theory to derive bounds on the entropy of fermionic reduced density matrices, a measure of the entanglement inherent to a fermionic quantum state.
", "doi": "10.7907/Z9D21VNV", "publication_date": "2017", "thesis_type": "phd", "thesis_year": "2017" }, { "id": "thesis:9763", "collection": "thesis", "collection_id": "9763", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05262016-092645359", "primary_object_url": { "basename": "Titum_Paraj_2016_thesis.pdf", "content": "final", "filesize": 9149970, "license": "other", "mime_type": "application/pdf", "url": "/9763/1/Titum_Paraj_2016_thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Disorder Driven Transitions in Non-Equilibrium Quantum Systems", "author": [ { "family_name": "Titum", "given_name": "Paraj", "orcid": "0000-0002-7792-1532", "clpid": "Titum-Paraj" } ], "thesis_advisor": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "thesis_committee": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Lindner", "given_name": "Netanel H.", "orcid": "0000-0003-1879-3902", "clpid": "Lindner-N-H" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.
\r\n\r\nIn periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.
\r\n \r\nInterestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.
\r\n \r\nFinally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.
\r\n \r\nThe thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach\r\nprovides a new framework to study the transition in this system.
", "doi": "10.7907/Z9MK69VV", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9172", "collection": "thesis", "collection_id": "9172", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09232015-145320310", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 13477843, "license": "other", "mime_type": "application/pdf", "url": "/9172/1/thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Coulomb Drag and Tunneling Studies in Quantum Hall Bilayers", "author": [ { "family_name": "Nandi", "given_name": "Debaleena", "clpid": "Nandi-Debaleena" } ], "thesis_advisor": [ { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" } ], "thesis_committee": [ { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" }, { "family_name": "Schwab", "given_name": "Keith C.", "orcid": "0000-0001-8216-4815", "clpid": "Schwab-K-C" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "The bilayer quantum Hall state at total filling factor \u03bdT=1, where the total electron density matches the degeneracy of the lowest Landau level, is a prominent example of Bose-Einstein condensation of excitons. A macroscopically ordered state is realized where an electron in one layer is tightly bound to a \"hole\" in the other layer. If exciton transport were the only bulk transportmechanism, a current driven in one layer would spontaneously generate a current of equal magnitude and opposite sign in the other layer. The Corbino Coulomb drag measurements presented in this thesis demonstrate precisely this phenomenon.
\r\n\r\nExcitonic superfluidity has been long sought in the \u03bdT=1 state. The tunneling between the two electron gas layers exihibit a dc Josephson-like effect. A simple model of an overdamped voltage biased Josephson junction is in reasonable agreement with the observed tunneling I-V. At small tunneling biases, it exhibits a tunneling \"supercurrent\". The dissipation is carefully studied in this tunneling \"supercurrent\" and found to remain small but finite.
", "doi": "10.7907/Z97H1GG0", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:10337", "collection": "thesis", "collection_id": "10337", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06072015-223040119", "primary_object_url": { "basename": "ShuPingLeeThesisv2.pdf", "content": "final", "filesize": 4200459, "license": "other", "mime_type": "application/pdf", "url": "/10337/1/ShuPingLeeThesisv2.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Signatures of Topological Superconductors", "author": [ { "family_name": "Lee", "given_name": "Shu-Ping", "orcid": "0000-0002-6199-2408", "clpid": "Lee-Shu-Ping" } ], "thesis_advisor": [ { "family_name": "Alicea", "given_name": "Jason", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" } ], "thesis_committee": [ { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors.
\r\n\r\nThe proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity.
\r\n\r\nThis system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction.
\r\n\r\nAs we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means.
\r\n\r\nApart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.
\r\n", "doi": "10.7907/Z90R9MB4", "publication_date": "2015", "thesis_type": "phd", "thesis_year": "2015" }, { "id": "thesis:8909", "collection": "thesis", "collection_id": "8909", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05282015-205532544", "primary_object_url": { "basename": "master.pdf", "content": "final", "filesize": 2124134, "license": "other", "mime_type": "application/pdf", "url": "/8909/1/master.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Numerical Studies of Topological Phases", "author": [ { "family_name": "Geraedts", "given_name": "Scott D.", "clpid": "Geraedts-Scott-D" } ], "thesis_advisor": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "thesis_committee": [ { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Alicea", "given_name": "Jason F.", "orcid": "0000-0001-9979-3423", "clpid": "Alicea-J" }, { "family_name": "Mong", "given_name": "Roger S.", "orcid": "0009-0000-7182-5681", "clpid": "Mong-Roger-S" }, { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "The topological phases of matter have been a major part of condensed matter physics research since the discovery of the quantum Hall effect in the 1980s. Recently, much of this research has focused on the study of systems of free fermions, such as the integer quantum Hall effect, quantum spin Hall effect, and topological insulator. Though these free fermion systems can play host to a variety of interesting phenomena, the physics of interacting topological phases is even richer. Unfortunately, there is a shortage of theoretical tools that can be used to approach interacting problems. In this thesis I will discuss progress in using two different numerical techniques to study topological phases.
\r\n\r\nRecently much research in topological phases has focused on phases made up of bosons. Unlike fermions, free bosons form a condensate and so interactions are vital if the bosons are to realize a topological phase. Since these phases are difficult to study, much of our understanding comes from exactly solvable models, such as Kitaev's toric code, as well as Levin-Wen and Walker-Wang models. We may want to study systems for which such exactly solvable models are not available. In this thesis I present a series of models which are not solvable exactly, but which can be studied in sign-free Monte Carlo simulations. The models work by binding charges to point topological defects. They can be used to realize bosonic interacting versions of the quantum Hall effect in 2D and topological insulator in 3D. Effective field theories of \"integer\" (non-fractionalized) versions of these phases were available in the literature, but our models also allow for the construction of fractional phases. We can measure a number of properties of the bulk and surface of these phases.
\r\n\r\nFew interacting topological phases have been realized experimentally, but there is one very important exception: the fractional quantum Hall effect (FQHE). Though the fractional quantum Hall effect we discovered over 30 years ago, it can still produce novel phenomena. Of much recent interest is the existence of non-Abelian anyons in FQHE systems. Though it is possible to construct wave functions that realize such particles, whether these wavefunctions are the ground state is a difficult quantitative question that must be answered numerically. In this thesis I describe progress using a density-matrix renormalization group algorithm to study a bilayer system thought to host non-Abelian anyons. We find phase diagrams in terms of experimentally relevant parameters, and also find evidence for a non-Abelian phase known as the \"interlayer Pfaffian\".
\r\n", "doi": "10.7907/Z9668B3N", "publication_date": "2015", "thesis_type": "phd", "thesis_year": "2015" }, { "id": "thesis:8462", "collection": "thesis", "collection_id": "8462", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06022014-093929164", "type": "thesis", "title": "Electronic States in Disordered Topological Insulators", "author": [ { "family_name": "Kim", "given_name": "Kun Woo", "clpid": "Kim-Kun-Woo" } ], "thesis_advisor": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "thesis_committee": [ { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Hsieh", "given_name": "David", "orcid": "0000-0002-0812-955X", "clpid": "Hsieh-David" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_eng" } ], "abstract": "We present a theoretical study of electronic states in topological insulators with impurities. Chiral edge states in 2d topological insulators and helical surface states in 3d topological insulators show a robust transport against nonmagnetic impurities. Such a nontrivial character inspired physicists to come up with applications such as spintronic devices [1], thermoelectric materials [2], photovoltaics [3], and quantum computation [4]. Not only has it provided new opportunities from a practical point of view, but its theoretical study has deepened the understanding of the topological nature of condensed matter systems. However, experimental realizations of topological insulators have been challenging. For example, a 2d topological insulator fabricated in a HeTe quantum well structure by Konig et al. [5] shows a longitudinal conductance which is not well quantized and varies with temperature. 3d topological insulators such as Bi2Se3 and Bi2Te3 exhibit not only a signature of surface states, but they also show a bulk conduction [6]. The series of experiments motivated us to study the effects of impurities and coexisting bulk Fermi surface in topological insulators. We first address a single impurity problem in a topological insulator using a semiclassical approach. Then we study the conductance behavior of a disordered topological-metal strip where bulk modes are associated with the transport of edge modes via impurity scattering. We verify that the conduction through a chiral edge channel retains its topological signature, and we discovered that the transmission can be succinctly expressed in a closed form as a ratio of determinants of the bulk Green's function and impurity potentials. We further study the transport of 1d systems which can be decomposed in terms of chiral modes. Lastly, the surface impurity effect on the local density of surface states over layers into the bulk is studied between weak and strong disorder strength limits.", "doi": "10.7907/BSH1-AA62", "publication_date": "2014", "thesis_type": "phd", "thesis_year": "2014" }, { "id": "thesis:7832", "collection": "thesis", "collection_id": "7832", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06042013-123144999", "primary_object_url": { "basename": "Alton_Thesis.pdf", "content": "final", "filesize": 425916860, "license": "other", "mime_type": "application/pdf", "url": "/7832/73/Alton_Thesis.pdf", "version": "v14.0.0" }, "type": "thesis", "title": "Interacting Single Atoms with Nanophotonics for Chip-Integrated Quantum Network", "author": [ { "family_name": "Alton", "given_name": "Daniel James", "clpid": "Alton-Daniel-James" } ], "thesis_advisor": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" } ], "thesis_committee": [ { "family_name": "Kimble", "given_name": "H. Jeff", "clpid": "Kimble-H-J" }, { "family_name": "Vahala", "given_name": "Kerry J.", "orcid": "0000-0003-1783-1380", "clpid": "Vahala-K-J" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Roukes", "given_name": "Michael Lee", "orcid": "0000-0002-2916-6026", "clpid": "Roukes-M-L" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "Underlying matter and light are their building blocks of tiny atoms and photons. The ability to control and utilize matter-light interactions down to the elementary single atom and photon level at the nano-scale opens up exciting studies at the frontiers of science with applications in medicine, energy, and information technology. Of these, an intriguing front is the development of quantum networks where N >> 1 single-atom nodes are coherently linked by single photons, forming a collective quantum entity potentially capable of performing quantum computations and simulations. Here, a promising approach is to use optical cavities within the setting of cavity quantum electrodynamics (QED). However, since its first realization in 1992 by Kimble et al., current proof-of-principle experiments have involved just one or two conventional cavities. To move beyond to N >> 1 nodes, in this thesis we investigate a platform born from the marriage of cavity QED and nanophotonics, where single atoms at ~100 nm near the surfaces of lithographically fabricated dielectric photonic devices can strongly interact with single photons, on a chip. Particularly, we experimentally investigate three main types of devices: microtoroidal optical cavities, optical nanofibers, and nanophotonic crystal based structures. With a microtoroidal cavity, we realized a robust and efficient photon router where single photons are extracted from an incident coherent state of light and redirected to a separate output with high efficiency. We achieved strong single atom-photon coupling with atoms located ~100 nm near the surface of a microtoroid, which revealed important aspects in the atom dynamics and QED of these systems including atom-surface interaction effects. We present a method to achieve state-insensitive atom trapping near optical nanofibers, critical in nanophotonic systems where electromagnetic fields are tightly confined. We developed a system that fabricates high quality nanofibers with high controllability, with which we experimentally demonstrate a state-insensitive atom trap. We present initial investigations on nanophotonic crystal based structures as a platform for strong atom-photon interactions. The experimental advances and theoretical investigations carried out in this thesis provide a framework for and open the door to strong single atom-photon interactions using nanophotonics for chip-integrated quantum networks.\r\n", "doi": "10.7907/Q8MQ-JC47", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7697", "collection": "thesis", "collection_id": "7697", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05102013-172241867", "primary_object_url": { "basename": "Thesis_IsaacKim_Final.pdf", "content": "final", "filesize": 2135749, "license": "other", "mime_type": "application/pdf", "url": "/7697/1/Thesis_IsaacKim_Final.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Conditional Independence in Quantum Many-Body Systems", "author": [ { "family_name": "Kim", "given_name": "Isaac Hyun", "clpid": "Kim-Isaac-Hyun" } ], "thesis_advisor": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" } ], "thesis_committee": [ { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application, some of these statements are generalized to quantum states that are approximately conditionally independent. These structures can be readily used in the studies of gapped quantum many-body systems, especially for the ones in two spatial dimensions. A number of rigorous results are derived, including (i) a universal upper bound for a maximal number of topologically protected states that is expressed in terms of the topological entanglement entropy, (ii) a first-order perturbation bound for the topological entanglement entropy that decays superpolynomially with the size of the subsystem, and (iii) a correlation bound between an arbitrary local operator and a topological operator constructed from a set of local reduced density matrices. I also introduce exactly solvable models supported on a three-dimensional lattice that can be used as a reliable quantum memory.", "doi": "10.7907/PZJN-A841", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7709", "collection": "thesis", "collection_id": "7709", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05142013-151159910", "primary_object_url": { "basename": "thesis_2013_marcus_teague_rev.pdf", "content": "final", "filesize": 6376567, "license": "other", "mime_type": "application/pdf", "url": "/7709/9/thesis_2013_marcus_teague_rev.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Scanning Tunneling Spectroscopic Studies on High-Temperature Superconductors and Dirac Materials", "author": [ { "family_name": "Teague", "given_name": "Marcus Lawrence", "clpid": "Teague-Marcus-Lawrence" } ], "thesis_advisor": [ { "family_name": "Yeh", "given_name": "Nai-Chang", "orcid": "0000-0002-1826-419X", "clpid": "Yeh-Nai-Chang" } ], "thesis_committee": [ { "family_name": "Yeh", "given_name": "Nai-Chang", "orcid": "0000-0002-1826-419X", "clpid": "Yeh-Nai-Chang" }, { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" }, { "family_name": "Libbrecht", "given_name": "Kenneth George", "orcid": "0000-0002-8744-3298", "clpid": "Libbrecht-K-G" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "This thesis details the investigations of the unconventional low-energy quasiparticle excitations in electron-type cuprate superconductors and electron-type ferrous superconductors as well as the electronic properties of Dirac fermions in graphene and three-dimensional strong topological insulators through experimental studies using spatially resolved scanning tunneling spectroscopy (STS) experiments.
\r\n\r\nMagnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type cuprate La0.1Sr0.9CuO2 (La-112) TC = 43 K, are investigated experimentally. For temperature (T) less than the superconducting transition temperature (TC), and in zero field, the quasiparticle spectra of La-112 exhibits gapped behavior with two coherence peaks and no satellite features. For magnetic field measurements at T < TC, first ever observation of vortices in La-112 are reported. Moreover, pseudogap-like spectra are revealed inside the core of vortices, where superconductivity is suppressed. The intra-vortex pseudogap-like spectra are characterized by an energy gap of VPG = 8.5 \u00b1 0.6 meV, while the inter-vortex quasiparticle spectra shows larger peak-to-peak gap values characterized by \u0394pk-pk(H) >VPG, and \u0394pk-pk (0)=12.2 \u00b1 0.8 meV > \u0394pk-pk (H > 0). The quasiparticle spectra are found to be gapped at all locations up to the highest magnetic field examined (H = 6T) and reveal an apparent low-energy cutoff at the VPG energy scale.
\r\n\r\nMagnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type \"122\" iron-based Ba(Fe1-xCox)2As2 are investigated for multiple doping levels (x = 0.06, 0.08, 0.12 with TC= 14 K, 24 K, and 20 K). For all doping levels and the T < TC, two-gap superconductivity is observed. Both superconducting gaps decrease monotonically in size with increasing temperature and disappear for temperatures above the superconducting transition temperature, TC. Magnetic resonant modes that follow the temperature dependence of the superconducting gaps have been identified in the tunneling quasiparticle spectra. Together with quasiparticle interference (QPI) analysis and magnetic field studies, this provides strong evidence for two-gap sign-changing s-wave superconductivity.
\r\n\r\nAdditionally spatial scanning tunneling spectroscopic studies are performed on mechanically exfoliated graphene and chemical vapor deposition grown graphene. In all cases lattice strain exerts a strong influence on the electronic properties of the sample. In particular topological defects give rise to pseudomagnetic fields (B ~ 50 Tesla) and charging effects resulting in quantized conductance peaks associated with the integer and fractional Quantum Hall States.
\r\n\r\nFinally, spectroscopic studies on the 3D-STI, Bi2Se3 found evidence of impurity resonance in the surface state. The impurities are in the unitary limit and the spectral resonances are localized spatially to within ~ 0.2 nm of the impurity. The spectral weight of the impurity resonance diverges as the Fermi energy approaches the Dirac point and the rapid recovery of the surface state suggests robust topological protection against perturbations that preserve time reversal symmetry.
\r\n", "doi": "10.7907/M8FW-S641", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7766", "collection": "thesis", "collection_id": "7766", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05292013-170142035", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 15890467, "license": "other", "mime_type": "application/pdf", "url": "/7766/1/thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "The Interplay of Localization and Interactions in Quantum Many-Body Systems", "author": [ { "family_name": "Iyer", "given_name": "Shankar", "clpid": "Iyer-Shankar" } ], "thesis_advisor": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "thesis_committee": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" }, { "family_name": "Cross", "given_name": "Michael Clifford", "clpid": "Cross-M-C" }, { "family_name": "Painter", "given_name": "Oskar J.", "orcid": "0000-0002-1581-9209", "clpid": "Painter-O" } ], "local_group": [ { "literal": "Institute for Quantum Information and Matter" }, { "literal": "div_pma" } ], "abstract": "Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.
\r\n\r\nThe first is the so-called \u201cdirty\u201d or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.
\r\n\r\nThe second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (\u201cergodic\u201d) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.
\r\n", "doi": "10.7907/37K7-6Q13", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:6024", "collection": "thesis", "collection_id": "6024", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09082010-155113346", "type": "thesis", "title": "Quantum Phases and Phase Transitions in Disordered Low-Dimensional Systems: Thin Film Superconductors, Bilayer Two-Dimensional Electron Systems, and One-Dimensional Optical Lattices", "author": [ { "family_name": "Zou", "given_name": "Yue", "clpid": "Zou-Yue" } ], "thesis_advisor": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" } ], "thesis_committee": [ { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Eisenstein", "given_name": "James P.", "orcid": "0000-0001-5460-0464", "clpid": "Eisenstein-J-P" }, { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The study of various quantum phases and the phase transitions between them in low-dimensional disordered systems has been a central theme of recent developments of condensed matter physics. Examples include disordered thin film superconductors, whose critical temperature and density of states can be affected by a normal metallic layer deposited on top of them; amorphous thin films exhibiting superconductor-insulator transitions (SIT) tuned by disorder or magnetic field; and bilayer two-dimensional electron systems at total filling factor \u03bd=1, which exhibit interlayer coherent quantum Hall state at small layer separation and have a phase transition tuned by layer separation, parallel magnetic field, density imbalance, or temperature. Although a lot of theoretical and experimental investigations have been done, many properties of these phases and natures of the phase transitions in these systems are still being debated. Here in this thesis, we report our progress towards a better understanding of these systems. For disordered thin film superconductors, we first propose that the experimentally observed lower-than-theory gap-Tc ratio in bilayer superconducting-normal-metal films is due to inhomogeneous couplings. Next, for films demonstrating superconductor-insulator transitions, we propose a new type of experiment, namely the drag resistance measurement, as a method capable of pointing to the correct theory among major candidates such as the quantum vortex picture and the percolation picture. For bilayer two-dimensional electron systems, we propose that a first-order phase transition scenario and the resulting Clausius-Clapeyron equations can describe various transitions observed in experiments quite well. Finally, in one-dimensional optical lattices, we show that one can engineer the long-sought-after random hopping model with only off-diagonal disorder by fast-modulating an Anderson insulator.", "doi": "10.7907/M4BX-7511", "publication_date": "2011", "thesis_type": "phd", "thesis_year": "2011" }, { "id": "thesis:1759", "collection": "thesis", "collection_id": "1759", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05122009-142703", "primary_object_url": { "basename": "Bishara-thesis.pdf", "content": "final", "filesize": 1247280, "license": "other", "mime_type": "application/pdf", "url": "/1759/2/Bishara-thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Non-Abelian Quantum Hall States and Fractional Statistics", "author": [ { "family_name": "Bishara", "given_name": "Waheb", "clpid": "Bishara-Waheb" } ], "thesis_advisor": [ { "family_name": "Nayak", "given_name": "Chetan", "clpid": "Nayak-C" } ], "thesis_committee": [ { "family_name": "Kitaev", "given_name": "Alexei", "orcid": "0000-0002-5777-642X", "clpid": "Kitaev-A" }, { "family_name": "Nayak", "given_name": "Chetan", "clpid": "Nayak-C" }, { "family_name": "Refael", "given_name": "Gil", "orcid": "0009-0007-4566-8441", "clpid": "Refael-G" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "The discovery of the fractional quantum Hall effect stimulated the investigation of anyons, particles with fractional statistics which are neither bosons nor fermions. This thesis focuses on the study of quantum Hall states which may support non-Abelian anyons. We first address the validity of assumptions used in the numerical study of such states, and then proceed with analyzing different experiments which can detect non-Abelian fractional statistics. We quantitatively analyze the two-point contact interferometer experiment, which is hoped to display clear-cut, direct evidence of non-Abelian fractional statistics. We calculate the temperature and voltage dependence of the interference experiment outcome, and the signal attenuation due to finite temperature loss of coherence. We then analyze the edge theory of a family of non-Abelian quantum Hall states in the second Landau level, and examine the tunneling between these states and a quantum dot. This tunneling problem maps onto the multi-channel Kondo problem, and will allow distinguishing between different quantum Hall states. Finally, we use the same theoretical methods for analyzing Sagnac interference in the conductance of a carbon nanotube loop, a one-dimensional system.\r\n", "doi": "10.7907/WQC4-W268", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:2410", "collection": "thesis", "collection_id": "2410", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06022008-222640", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 5953369, "license": "other", "mime_type": "application/pdf", "url": "/2410/1/thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Probing Electronic Properties of Carbon Nanotubes", "author": [ { "family_name": "Heo", "given_name": "Jinseong", "clpid": "Heo-Jinseong" } ], "thesis_advisor": [ { "family_name": "Bockrath", "given_name": "Marc William", "clpid": "Bockrath-M-W" } ], "thesis_committee": [ { "family_name": "Yeh", "given_name": "Nai-Chang", "orcid": "0000-0002-1826-419X", "clpid": "Yeh-Nai-Chang" }, { "family_name": "Fultz", "given_name": "Brent T.", "orcid": "0000-0002-6364-8782", "clpid": "Fultz-B-T" }, { "family_name": "Bockrath", "given_name": "Marc William", "clpid": "Bockrath-M-W" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-Olexei" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Carbon nanotubes are quasi-one-dimensional objects that have many remarkable electronic properties. In Chapter I, an electrostatic force microscopy technique to probe the local density of states of single-walled carbon nanotubes (SWCNTs) under ambient conditions is described. Coupling the atomic force microscope tip motion with the quantum capacitance of nanotubes enables the van Hove singularities in the one-dimensional density of states to be resolved. We utilized this technique to identify individual semiconducting and metallic tubes, and further to estimate the chiral angle of a nanotube. Moreover, in order to realize a SWCNT interferometer, nanotube loop devices where a self-crossing geometry yields two electron paths that is a possible analog of the optical Sagnac interferometer are fabricated and explored in Chapter II. Scanning gate microscopy reveals for semiconducting devices a 0\u201350% transmission probability into the loop segment at the junction, which can be controlled by applying back gate voltage, hence shifting the Fermi level of the nanotube. Metallic loop devices having low contact resistance showed a large- scale conductance peak with fast oscillations superposed on it. Possible theoretical explanations including Sagnac-type interference, which takes the velocity difference between left and right movers in to account, and Fabry-Perot-type interference are compared with the experimental observations. In Chapter III, in accordance with increasing demand for developing spin-electronic devices, cobalt-filled multi-walled carbon nanotubes (Co\u2013filled MWCNTs) are first synthesized and imaged by transmission electron microscopy, and also characterized by various spectroscopy tools like X\u2013ray diffraction and energy dispersive X\u2013ray spectrometry. Further, a Co\u2013filled MWCNT device having reproducible switching in magnetoresistance was demonstrated. The last topic, in Chapter IV, covers the effects of a transverse electric field in MWCNT devices, where conductance fluctuations as a function of the transverse electric field were observed. The electric field spacing between the peaks of the fluctuations is in agreement with the theoretical predictions of band structure modulation by transverse electric fields. Future work following our experimental studies is proposed and discussed at the end of each chapter.", "doi": "10.7907/A83N-TN35", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" } ]