Total correlations of the diagonal ensemble herald the many-body localization transition

TL;DR

This paper introduces the use of total correlations from quantum information theory as a new diagnostic tool to characterize the many-body localization transition, revealing distinct scaling behaviors in different phases.

Contribution

The study applies total correlations to the diagonal ensemble to effectively identify and analyze the MBL transition, providing a novel quantitative approach.

Findings

Total correlations scale sub-linearly in ergodic phases.

Total correlations scale extensively in localized phases.

A pronounced peak at the transition point indicates ergodicity breaking.

Abstract

The intriguing phenomenon of many-body localization (MBL) has attracted significant interest recently, but a complete characterization is still lacking. In this work, we introduce the total correlations, a concept from quantum information theory capturing multi-partite correlations, to the study of this phenomenon. We demonstrate that the total correlations of the diagonal ensemble provides a meaningful diagnostic tool to pin-down, probe, and better understand the MBL transition and ergodicity breaking in quantum systems. In particular, we show that the total correlations has sub-linear dependence on the system size in delocalized, ergodic phases, whereas we find that it scales extensively in the localized phase developing a pronounced peak at the transition. We exemplify the power of our approach by means of an exact diagonalization study of a Heisenberg spin chain in a disordered field.