A theory of many-body localization in periodically driven systems

Dmitry Abanin; Wojciech De Roeck; François Huveneers

doi:10.1016/j.aop.2016.03.010

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arXiv · 1412.4752

A theory of many-body localization in periodically driven systems

Dmitry Abanin·Wojciech De Roeck·François Huveneers

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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.

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Dmitry Abanin, Wojciech De Roeck, François Huveneers. 2014-12-15. A theory of many-body localization in periodically driven systems. https://doi.org/10.1016/j.aop.2016.03.010

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