Mean field theory of failed thermalizing avalanches

TL;DR

This paper develops a mean field theory to analyze the stability of localization in quasiperiodic two-dimensional systems with ergodic grains, contrasting with random systems where avalanches cause thermalization.

Contribution

It introduces a self-consistent entanglement mean field theory that accurately predicts entanglement distributions and dynamical observables, extending understanding of localization stability.

Findings

Localization remains stable with finite ergodic grains in quasiperiodic systems.

The theory reproduces exact diagonalization data.

Predicts the spatial profile of failed avalanches.

Abstract

We show that localization in quasiperiodically modulated, two-dimensional systems is stable to the presence of a finite density of ergodic grains. This contrasts with the case of randomly modulated systems, where such grains seed thermalizing avalanches. These results are obtained within a quantitatively accurate, self-consistent entanglement mean field theory which analytically describes two level systems connected to a central ergodic grain. The theory predicts the distribution of entanglement entropies of each two level system across eigenstates, and the late time values of dynamical observables. In addition to recovering the known phenomenology of avalanches, the theory reproduces exact diagonalization data, and predicts the spatial profile of the thermalized region when the avalanche fails.