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Many-Body Localization in Strongly Correlated Systems

Yarloo, Hadi | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 52542 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Langari, Abdollah
  7. Abstract:
  8. Thermalizing quantum systems are conventionally described by statistical mechanics at equilibrium. In contrast, the interplay of disorder and interactions leads to manybody localization (MBL) which avoids thermalization in a closed quantum system.This phenomenon is the only known generic mechanism in which the “eigenstate thermalization hypothesis” is violated. In this vein, localization can protect quantum order even in finite temperature and create emergent nonergodic phases (e.g., time crystal), having no equilibrium counterpart. Yet in the conventional wisdom, the presence of disorder along with the excellent isolation from thermal bath are both necessary for the appearance of the MBL.In this thesis, we abolish these common believes and supply clear-cut evidences that a nonergodic dynamics, and the resulting localization protected order, can be found in a minimal model dropping all the essential ingredients needed for the existence of the MBL.As a first example, we identify anyonic self-induced localization in a family of clean self-correcting quantum memories, whose elementary excitations are associated with Abelian anyons. Using a non-perturbative approach, we demonstrate that nontrivial anyonic statistics can effectively induce self-generated disorder which intrinsically suppresses the diffusion of them for exponentially long time. The anyonic self-localization can impede logical error which is one of the major obstacles toward identifying a stable low-dimensional quantum memory.In the next example, we expand the machinery of self-localization to the realm of lattice gauge theory (LGT) which is one of the fundamental theory both in the condensed matter and particle physics. To this end, we introduce a clean spin-fermion model, forming an unconstrained Z2 LGT. We argue that the dynamical properties of the matter fields can be controlled by the initial entanglement structure of the gauge fields. Indeed, for any starting product state, the matters exhibit dynamical localization, which is driven solely by interaction, and thus is of a pure dynamical many-body effect. However, the matter degrees of freedom are embedded throughout the fully thermalizing gauge fields in a disentangled manner.In order to extend these ideas, we turn to investigate a clean Floquet model whose quasi-spectrum conforms to the ergodic Wigner-Dyson distribution, yet having a robust temporal crystalline order with strong initial-state dependence. We relate such behavior to the rare existence of some non-thermal Floquet eigenstates, having the long range correlations, which are embedded in the thermalizing Floquet spectrum and develop a high overlap with a family of short-range correlated initial states. We dub such crystalline dynamics, rooted in the weak breakdown of ergodicity, “scarred discrete time crystal”
  9. Keywords:
  10. Time Crystals ; Many Body Localization ; Many Body Scars ; Out-of-Equilibrium Phases

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