Thouless time analysis of Anderson and many-body localization transitions

TL;DR

This paper investigates the spectral statistics of disordered quantum systems to understand the transition between chaotic and localized phases, revealing breakdowns in scaling near the localization transition.

Contribution

It introduces a Thouless time analysis for Anderson and many-body localization transitions, highlighting the limitations of two-parameter scaling near the transition point.

Findings

Two-parameter scaling breaks down near the localization transition.

Thouless time scaling reveals subdiffusive dynamics.

Results connect spectral statistics with localization phenomena.

Abstract

Spectral statistics of disordered systems encode Thouless and Heisenberg time scales whose ratio determines whether the system is chaotic or localized. Identifying similarities between system size and disorder strength scaling of Thouless time for disordered quantum many-body systems with results for 3D and 5D Anderson models, we argue that the two-parameter scaling breaks down in the vicinity of the transition to the localized phase signalling subdiffusive dynamics.