The fate of dynamical many-body localization in the presence of disorder

TL;DR

The paper investigates how dynamical many-body localization persists or is destroyed in disordered quantum systems under periodic driving, revealing conditions where localization effects significantly slow down relaxation despite disorder.

Contribution

It demonstrates that certain parameter regimes under periodic drive can cause exponential divergence of relaxation times, indicating persistent localization effects even with strong disorder.

Findings

Relaxation time $ au$ increases dramatically at specific drive parameters.

$ au$ diverges exponentially with drive frequency $oldsymbol{}$ when ratio $oldsymbol{h_0/}$ is fixed.

Dynamical localization remnants survive strong disorder under certain conditions.

Abstract

Dynamical localization is one of the most startling manifestations of quantum interference, where the evolution of a simple system is frozen out under a suitably tuned coherent periodic drive. Here, we show that, although any randomness in the interactions of a many body system kills dynamical localization eventually, spectacular remnants survive even when the disorder is strong. We consider a disordered quantum Ising chain where the transverse magnetization relaxes exponentially with time with a decay time-scale $\tau$ due to random longitudinal interactions between the spins. We show that, under external periodic drive, this relaxation slows down ($\tau$ shoots up) by orders of magnitude as the ratio of the drive frequency $\omega$ and amplitude $h_{0}$ tends to certain specific values (the freezing condition). If $\omega$ is increased while maintaining the ratio $h_0/\omega$ at a fixed freezing value, then $\tau$ diverges exponentially with $\omega.$ The results can be easily extended for a larger family of disordered fermionic and bosonic systems.