Many body localization transition with correlated disorder

TL;DR

This paper investigates how spatially correlated disorder affects the many-body localization transition in one-dimensional systems, finding that anticorrelations are irrelevant and positive correlations do not alter the critical theory.

Contribution

It extends the understanding of MBL transition by analyzing the impact of correlated disorder, showing that anticorrelations are irrelevant and positive correlations do not change the critical behavior.

Findings

Anticorrelated disorder is irrelevant at the MBL transition.

Positively correlated disorder does not alter the critical theory.

Correlations modify properties within the localized phase.

Abstract

We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. We consider a general family of disorder models, parameterized by how strong the fluctuations of the disordered couplings are when coarse-grained over a region of size $\ell$. For uncorrelated randomness, the characteristic scale for these fluctuations is $\sqrt{\ell}$; more generally they scale as $\ell^\gamma$. We discuss both positively correlated disorder ($1/2 < \gamma < 1$) and anticorrelated, or "hyperuniform," disorder ($\gamma < 1/2$). We argue that anticorrelations in the disorder are generally irrelevant at the MBL transition. Moreover, assuming the MBL transition is described by the recently developed renormalization-group scheme of Morningstar \emph{et al.} [Phys. Rev. B 102, 125134, (2020)], we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase.