Thouless energy and multifractality across the many-body localization transition

TL;DR

This paper investigates the many-body localization transition by analyzing matrix elements, revealing a broad critical region with multifractality and a breakdown of thermalization, providing new insights into the critical behavior of disordered quantum systems.

Contribution

It introduces a detailed analysis of off-diagonal matrix elements across the MBL transition, identifying a critical region with multifractality and elucidating the behavior of the Thouless energy.

Findings

Identification of a wide critical region around the MBL transition

Observation of multifractality in matrix elements during the transition

Thouless energy becomes smaller than level spacing in the critical region

Abstract

Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across the many-body localization transition (MBLT) in a disordered spin chain, and use it to characterize the breakdown of the eigenstate thermalization hypothesis and to extract the many-body Thouless energy. We find a wide critical region around the MBLT, where Thouless energy becomes smaller than the level spacing, while matrix elements show critical dependence on the energy difference. In the same region, matrix elements, viewed as amplitudes of a fictitious wave function, exhibit strong multifractality. Our findings show that the correlation length becomes larger than the accessible system sizes in a broad range of disorder strength values, and shed light on the critical behaviour of MBL systems.