Thermal avalanches in isolated many-body localized systems

TL;DR

This paper investigates the stability of many-body localization in disordered spin chains, revealing that thermal avalanches depend on the relative size of thermal regions and disorder strength, with an intermediate phase observed at finite sizes.

Contribution

It provides a numerical analysis of thermal avalanches in many-body localized systems, highlighting the conditions under which localization is destabilized and identifying an intermediate phase.

Findings

Avalanche occurs only if thermal region scales with system size at strong disorder.

An intermediate phase exists between localization and ergodicity at finite sizes.

Results suggest these phenomena persist in the thermodynamic limit.

Abstract

Many-body localization is a profound phase of matter affecting the entire spectrum which emerges in the presence of disorder in interacting many-body systems. Recently, the stability of many-body localization has been challenged by the avalanche mechanism, in which a small thermal region can spread, destabilizing localization and leading to global thermalization of the system. A key unresolved question is the critical competition between the thermal region's influence and the disorder strength required to trigger such an avalanche. Here, we numerically investigate many-body localization stability in an isolated Heisenberg spin chain of size $L$ subjected to a disordered magnetic field. By embedding a tunable thermal region of size $P$, we analyze the system's behavior in both static and dynamical regimes using entanglement entropy and the gap ratio. Our study yields two main findings. Firstly, for strong disorder, the avalanche only occurs if the thermal region scales with system size, specifically when $P/L$ exceeds a threshold value. Secondly, at strong disorder, we identify an intermediate phase between many-body localization and ergodic behavior as $P$ increases. This intermediate phase leaves its finger print in both static and dynamic properties of the system and tends to vanish in the thermodynamic limit. Although our simulations are restricted to finite system sizes, the analysis suggests that these results hold in the thermodynamic limit for isolated many-body systems.