A theory of many-body localization in periodically driven systems

TL;DR

This paper develops a theoretical framework for understanding many-body localization in periodically driven quantum systems, showing that MBL can persist at high frequencies and proposing a phase diagram for driven MBL phases.

Contribution

The paper introduces a theory demonstrating that MBL persists under high-frequency periodic driving by representing the Floquet operator as an exponential of an effective MBL Hamiltonian.

Findings

MBL persists at high driving frequencies

Effective Hamiltonian remains fully MBL under periodic driving

Delocalization occurs at low driving frequencies

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.