Thermalization propagation front and robustness against avalanches in localized systems

TL;DR

This paper studies the slow propagation of thermalization in many-body localized systems, showing that MBL remains robust against avalanches due to logarithmically slow thermalization fronts.

Contribution

It introduces a method to analyze the thermalization front dynamics and demonstrates MBL robustness against avalanches over broad parameter ranges.

Findings

Thermalization front propagates logarithmically slowly in time.

MBL phase remains stable against avalanches in certain parameter regimes.

Imbalance thermalizes exponentially slowly with disorder and system size.

Abstract

We investigate the robustness of the many-body localized (MBL) phase to the quantum-avalanche instability by studying the dynamics of a localized spin chain coupled to a $T=\infty$ thermal bath through its leftmost site. By analyzing local magnetizations, we estimate the size of the thermalized sector of the chain and find that it increases logarithmically slowly in time. This logarithmically slow propagation of the thermalization front allows us to lower bound the slowest thermalization time, and find a broad parameter range where it scales fast enough with the system size that MBL is robust against thermalization induced by avalanches. The further finding that the imbalance -- a global quantity measuring localization -- thermalizes over a time scale exponential both in disorder strength and system size is in agreement with these results.