Many-body localized to ergodic transitions in a system with correlated disorder

TL;DR

This paper investigates the transition from many-body localized to ergodic phases in a spin chain with correlated disorder, revealing how correlations influence the phase boundary and introducing a unifying parameter for analysis.

Contribution

It introduces a single parameter based on sample variance to characterize correlated disorder effects and analytically derives the phase diagram for the transition.

Findings

Transition point shifts with disorder and correlation strength.

Sample variance average collapses multiple statistical measures.

Analytical phase diagram matches numerical results.

Abstract

We study the transition from a many-body localized phase to an ergodic phase in spin chain with correlated random magnetic fields. Using multiple statistical measures like gap statistics and extremal entanglement spectrum distributions, we find the phase diagram in the disorder-correlation plane, where the transition happens at progressively larger values of the correlation with increasing values of disorder. We then show that one can use the average of sample variance of magnetic fields as a single parameter which encodes the effects of the correlated disorder. The distributions and averages of various statistics collapse into a single curve as a function of this parameter. This also allows us to analytically calculate the phase diagram in the disorder-correlation plane.