Avalanche induced co-existing localised and thermal regions in disordered chains

TL;DR

This paper studies how a small thermal region can destabilize an Anderson localized chain, leading to a partially thermalized, non-ergodic phase, with theoretical predictions confirmed through numerical simulations.

Contribution

It introduces a new framework for understanding avalanche instability in disordered chains and derives the critical conditions for thermalization onset.

Findings

Thermal seed causes runaway thermalization above a critical localization length.

The seed size required for avalanche diverges at the threshold.

Numerical simulations confirm avalanche theory predictions in Anderson chains.

Abstract

We investigate the stability of an Anderson localized chain to the inclusion of a single finite interacting thermal seed. This system models the effects of rare low-disorder regions on many-body localized chains. Above a threshold value of the mean localization length, the seed causes runaway thermalization in which a finite fraction of the orbitals are absorbed into a thermal bubble. This `partially avalanched' regime provides a simple example of a delocalized, non-ergodic dynamical phase. We derive the hierarchy of length scales necessary for typical samples to exhibit the avalanche instability, and show that the required seed size diverges at the avalanche threshold. We introduce a new dimensionless statistic that measures the effective size of the thermal bubble, and use it to numerically confirm the predictions of avalanche theory in the Anderson chain at infinite temperature.