Regimes of heating and dynamical response in driven many-body localized systems

TL;DR

This paper investigates how many-body localized systems respond to periodic driving, revealing regimes of linear and nonlinear heating and their implications for the phase transition near MBL.

Contribution

It introduces a generalized heating rate for driven MBL systems, combining numerical and analytical methods to explore response regimes across different drive amplitudes.

Findings

Linear response proportional to optical conductivity at small amplitudes

Nonlinear power-law heating at large amplitudes

Crossover mechanisms in MBL phase and near transition

Abstract

We explore the response of many-body localized (MBL) systems to periodic driving of arbitrary amplitude, focusing on the rate at which they exchange energy with the drive. To this end, we introduce an infinite-temperature generalization of the effective "heating rate" in terms of the spread of a random walk in energy space. We compute this heating rate numerically and estimate it analytically in various regimes. When the drive amplitude is much smaller than the frequency, this effective heating rate is given by linear response theory with a coefficient that is proportional to the optical conductivity; in the opposite limit, the response is nonlinear and the heating rate is a nontrivial power-law of time. We discuss the mechanisms underlying this crossover in the MBL phase, and comment on its implications for the subdiffusive thermal phase near the MBL transition.