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UC Berkeley UC Berkeley Electronic Theses and Dissertations UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Quantum Phenomena in Interacting Many-Body Systems: Topological Protection, Localization, and Non-Fermi Liquids Permalink https://escholarship.org/uc/item/9kw3g8gg Author Bahri, Yasaman Publication Date 2017 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Quantum Phenomena in Interacting Many-Body Systems: Topological Protection, Localization, and Non-Fermi Liquids by Yasaman Bahri A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Ashvin Vishwanath, Chair Professor Joel Moore Professor K. Birgitta Whaley Spring 2017 Quantum Phenomena in Interacting Many-Body Systems: Topological Protection, Localization, and Non-Fermi Liquids Copyright 2017 by Yasaman Bahri 1 Abstract Quantum Phenomena in Interacting Many-Body Systems: Topological Protection, Localization, and Non-Fermi Liquids by Yasaman Bahri Doctor of Philosophy in Physics University of California, Berkeley Professor Ashvin Vishwanath, Chair This dissertation establishes and investigates new phenomena in diverse interacting many- body quantum systems guided by three distinct, but complementary, themes: (i) symmetry and topology, (ii) localization, and (iii) non-Fermi liquids. The first theme concerns how the interplay of symmetry and topology can offer robust protection for a many-body system. We investigate low-dimensional quantum fermionic mod- els from a general structural perspective. These phases can exhibit fractionalized Majorana zero-energy modes on their boundary. We devise experimentally relevant nonlocal measure- ments that can be used to detect these topological phases. While our primary focus is on quantum systems, topologically protected behavior can arise in classical mechanical models as well. We extend a recent connection between the topological band theory of electrons and classical physics by proposing a mechanical analogue of a topological nodal semimetal. The second theme concerns that of many-body localization. We demonstrate that the combination of localization, symmetry, and topology can have radical consequences for quan- tum systems at high energies, such as the existence of protected gapless boundary modes. We show that, even at these high energies, quantum information can be preserved, and quantum coherence recovered. Quantum coherent dynamics in this regime is unexpected and of great interest for quantum computation. The third direction in our study of interacting many-body systems concerns non-Fermi liquids. We construct a non-Fermi liquid by bringing together a spin-orbit coupled Fermi surface and fluctuating magnetic order. Using newly developed analytic tools for strongly coupled systems, we demonstrate the stability of the non-Fermi liquid to ordering. This identifies an experimentally accessible candidate for exploring physics that lies beyond Fermi liquid theory. i To my teachers ii Contents Contents ii 1 Introduction 1 2 Nonlocal Order Parameters for Quasi-1D Phases with Majorana Edge Modes 5 2.1 Symmetry-Protected Topological Phases . 6 2.2 Nonlocal Order Parameters . 10 2.3 String and Brane Order for Majorana Chains . 13 2.4 Quasi-1D Phases with ZN Translation Symmetry . 19 2.5 Measuring Nonlocal Order in Ultracold Atomic Systems . 28 2.6 Conclusion . 32 2.7 Appendix A: Applying a Broken Symmetry on a Domain . 33 2.8 Appendix B: Fermionic Classification . 33 2.9 Appendix C: Fermionic Selection Rules . 34 3 Many-body Localization, Topological Phases, and Quantum Coherence 36 3.1 Introduction to Many-Body Localization . 37 3.2 Emergent Local Integrability . 41 3.3 Order Protected by Localization . 43 3.4 A 1D Model for SPT-MBL . 45 3.5 Quantum Dynamics and Spin Echo . 50 3.6 Conclusion . 52 3.7 Appendix A: Analysis of Spin Echo Protocol . 53 3.8 Appendix B: Additional Figures . 56 4 Construction of a Stable Non-Fermi Liquid Phase 59 4.1 Fermi Liquids . 59 4.2 Non-Fermi Liquids . 62 4.3 Coupling a Spin-Orbit Fermi Surface to Fluctuating Magnetization . 65 4.4 Landau Damping and the Breakdown of Electron Quasiparticles . 69 4.5 Stability of the Non-Fermi Liquid Phase to Order . 70 iii 4.6 Experimental Considerations . 74 4.7 Conclusion . 77 4.8 Appendix A: Boson Polarization and Electron Self-Energy . 78 4.9 Appendix B: Patch Susceptibilities . 81 4.10 Appendix C: Disorder Effects and Calculation of Resistivity . 86 5 A Mechanical Analogue of Topological Nodal Semimetals 90 5.1 Introduction to Topological Mechanics . 91 5.2 Construction of our Model . 93 5.3 Dispersion and Robustness of Zero Modes . 97 5.4 An Alternative Model . 100 5.5 Conclusion . 102 Bibliography 103 iv Acknowledgments I would first like to express my deepest gratitude to my advisor Ashvin Vishwanath for his mentorship. It has been a privilege to be his student. It goes without saying that Ashvin is an exceptionally creative and deep thinker with an overabundance of very interesting research ideas. I have been and remain continually amazed at how Ashvin seeks out and targets the most interesting and important attributes of any problem, always clearly distill- ing new physics from the old. He is also very generous and humble. His attitude towards research and discovery, as well as his taste in problems and his emphasis on inventive work, have been influential beyond measure. Ashvin fostered and led a highly stimulating research environment at Berkeley during my time in graduate school. I will always be grateful to him for a singularly rewarding experience and his unfailing support and encouragement of me. Several individuals also played important roles in the topics of this dissertation. I would like to thank Ehud Altman for many interesting discussions and an enjoyable collabora- tion, not to mention his thoughtful and considerate guidance over time. In particular, Ehud brought to Berkeley new ideas and problems on many-body localization and quantum dy- namics during his extended stay in 2013, leading to some of the material contained herein. I thank Andrew Potter for the opportunity to collaborate on a project on non-Fermi liquids. Andrew is a gifted researcher with a broad knowledge of condensed matter, and through this project I was introduced to field theoretic developments for strongly coupled systems. I would also like to thank Adrian Po, a most curious and perceptive collaborator, for a joint project on topological mechanical models. I thank Birgitta Whaley and Joel Moore for serving on my dissertation committee, as well as for expressing interest in my work and in my scientific development. I thank all those who passed through Berkeley's condensed matter theory group. Among current and former postdocs and visitors, I particularly appreciate interactions with Andrew Potter, Sid Parameswaran, Frank Pollmann, Norman Yao, Tarun Grover, Maksym Serbyn, Snir Gazit, Xie Chen, Yuan-Ming Lu, and Lukasz Fidkowski. Amongst fellow students, I would particularly like to thank Itamar Kimchi, Michael Zaletel, Gil Young Cho, and Charles Xiong. It is a pleasure to especially thank three individuals { Adrian Po, Philipp Dumitrescu, and Haruki Watanabe { who kindly shared their insights and understanding on many occa- sions. Their presence made my research experience quite a rich and memorable one. Looking farther back, I am indebted to Joel Moore for an early and rare research op- portunity during my final undergraduate year at Berkeley. Joel is a patient teacher, and I learned much through that experience. It was also my introduction to quantum tensor net- works, which lie at an intersection of quite exciting ideas. That research experience paved v the way for subsequent opportunities in condensed matter theory, which I very much wanted to continue in, following graduation. I could not have chosen a more perfect field than this one, and I thank Joel for having played the pivotal role in that. I would like to thank professors in the Physics Department at Berkeley whose teaching during my undergraduate years was influential during my physics studies: Robert Littlejohn, Dung-Hai Lee, Martin White, and Steven Louie. Finally, I give thanks to my family for seeing me through many years of education. To my mother for her involvement in my learning during the early years. To my younger brother for his encouragement and steadfast good humor, especially during my time in graduate school. This dissertation is dedicated to all the teachers I have had throughout my life, and especially those who, directly or indirectly, aided or encouraged me in the pursuit of physics. 1 Chapter 1 Introduction The many-body interacting systems found in condensed matter settings are a fascinating playground for theoretical study. A traveler to this domain discovers some of the richest behavior in the physical world that is nonetheless describable by a rather unified body of theory. Such a balance between diversity and complexity, on the one hand, and theory that is both tractable and powerfully predictive, on the other, is a rare find in the scientific world. This dissertation, like condensed matter itself, is rather broad in scope. Each of the subsequent chapters here covers a distinct direction of current interest in the field. The focus is almost entirely on quantum systems. There are a few overarching themes that we wish to highlight because they play a fundamental role, both in this dissertation and more broadly: Entanglement Quantum entanglement lies at the heart of many problems. Entanglement has shed a great deal of light on why some states are similar and some are different, by allowing us to abstract away particularities of a wavefunction { such as the degrees of freedom that it is composed of, or the exact amplitudes of an expansion { and understand instead the bare structural com- plexity, the skeleton of quantum states. As we will survey in this dissertation, entanglement plays a fundamental role in how a quantum system thermalizes; it provides an underlying classification for quantum phases; and an understanding of it allows us to identify correct parameterizations for large classes of quantum states.
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