Theory of manybody localization in periodically driven systems
Abstract
We present a theory of periodically driven, manybody 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 timeindependent Hamiltonian, which is a sum of quasilocal terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the timedependence 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 manybody 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:
 Department of Theoretical Physics, University of Geneva (Switzerland)
 Instituut voor Theoretische Fysica, KU Leuven (Belgium)
 CEREMADE, Université ParisDauphine (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; MANYBODY PROBLEM; PERIODICITY; PHASE DIAGRAMS; TIME DEPENDENCE
Citation Formats
Abanin, Dmitry A., Email: dabanin@gmail.com, De Roeck, Wojciech, and Huveneers, François. Theory of manybody localization in periodically driven systems. United States: N. p., 2016.
Web. doi:10.1016/J.AOP.2016.03.010.
Abanin, Dmitry A., Email: dabanin@gmail.com, De Roeck, Wojciech, & Huveneers, François. Theory of manybody localization in periodically driven systems. United States. doi:10.1016/J.AOP.2016.03.010.
Abanin, Dmitry A., Email: dabanin@gmail.com, De Roeck, Wojciech, and Huveneers, François. 2016.
"Theory of manybody localization in periodically driven systems". United States.
doi:10.1016/J.AOP.2016.03.010.
@article{osti_22617368,
title = {Theory of manybody localization in periodically driven systems},
author = {Abanin, Dmitry A., Email: dabanin@gmail.com and De Roeck, Wojciech and Huveneers, François},
abstractNote = {We present a theory of periodically driven, manybody 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 timeindependent Hamiltonian, which is a sum of quasilocal terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the timedependence 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 manybody 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 = 2016,
month = 9
}

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