Many-body delocalization as a quantum avalanche

TL;DR

This paper introduces a multi-scale diagonalization approach to analyze the MBL-ergodic transition in disordered 1D chains, highlighting the role of resonant spots and quantum avalanches in localization and delocalization phenomena.

Contribution

It presents a novel multi-scale diagonalization scheme and analytical insights into the critical behavior of many-body localization transitions.

Findings

Localization probability is one at criticality under certain assumptions.

Delocalization occurs via quantum avalanches triggered by large ergodic spots.

A power-law distribution of thermal inclusions is predicted at the transition.

Abstract

We propose a multi-scale diagonalization scheme to study disordered one-dimensional chains, in particular the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots. Our scheme focuses on the dichotomy MBL versus {ETH} (eigenstate thermalization hypothesis). We show that a few natural assumptions imply that the system is localized with probability one at criticality. On the ergodic side, delocalization is induced by a quantum avalanche seeded by large ergodic spots, whose size diverges at the transition. On the MBL side, the typical localization length tends to a finite universal value at the transition, but there is a divergent length scale related to the response to an inclusion of large ergodic spots. A mean field approximation analytically illustrates these results and predicts as a power-law distribution for thermal inclusions at criticality.