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Title: Theory of many-body localization in periodically driven systems

Abstract

We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.

Authors:
 [1];  [2];  [3]
  1. Department of Theoretical Physics, University of Geneva (Switzerland)
  2. Instituut voor Theoretische Fysica, KU Leuven (Belgium)
  3. CEREMADE, Université Paris-Dauphine (France)
Publication Date:
OSTI Identifier:
22617368
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 372; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CANONICAL TRANSFORMATIONS; HAMILTONIANS; MANY-BODY PROBLEM; PERIODICITY; PHASE DIAGRAMS; TIME DEPENDENCE

Citation Formats

Abanin, Dmitry A., E-mail: dabanin@gmail.com, De Roeck, Wojciech, and Huveneers, François. Theory of many-body localization in periodically driven systems. United States: N. p., 2016. Web. doi:10.1016/J.AOP.2016.03.010.
Abanin, Dmitry A., E-mail: dabanin@gmail.com, De Roeck, Wojciech, & Huveneers, François. Theory of many-body localization in periodically driven systems. United States. doi:10.1016/J.AOP.2016.03.010.
Abanin, Dmitry A., E-mail: dabanin@gmail.com, De Roeck, Wojciech, and Huveneers, François. Thu . "Theory of many-body localization in periodically driven systems". United States. doi:10.1016/J.AOP.2016.03.010.
@article{osti_22617368,
title = {Theory of many-body localization in periodically driven systems},
author = {Abanin, Dmitry A., E-mail: dabanin@gmail.com and De Roeck, Wojciech and Huveneers, François},
abstractNote = {We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.},
doi = {10.1016/J.AOP.2016.03.010},
journal = {Annals of Physics},
number = ,
volume = 372,
place = {United States},
year = {Thu Sep 15 00:00:00 EDT 2016},
month = {Thu Sep 15 00:00:00 EDT 2016}
}