Early breakdown of area-law entanglement at many-body delocalization transition

TL;DR

This paper introduces a new numerical method to study the many-body localization transition, revealing that previous finite size studies likely underestimated the critical disorder needed for delocalization.

Contribution

The authors develop the numerical linked cluster expansion as a controlled, thermodynamic limit approach for analyzing MBL transitions without finite size scaling.

Findings

Critical disorder value is higher than previous estimates.

Finite size effects tend to overestimate the localized phase.

The mobility edge remains consistent across energies examined.

Abstract

We introduce the numerical linked cluster (NLC) expansion as a controlled numerical tool for the study of the many-body localization (MBL) transition in a disordered system with continuous non-perturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and find that our conclusion is the same at all examined energies.