A 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.

8 pages, 3 figures. Presentation improved, appendix added

References in corpus (8)

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• Localization of interacting fermions at high temperature
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Periodically driven ergodic and many-body localized quantum systems
• Stability of a Floquet Bose-Einstein condensate in a one-dimensional optical lattice

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