Entanglement critical length at the many-body localization transition

TL;DR

This paper investigates how the entanglement spectrum distribution in a disordered spin chain changes with system size and disorder strength, revealing a divergence of the correlation length at the many-body localization transition.

Contribution

It introduces a detailed analysis of the entanglement spectrum distribution and identifies a correlation length diverging at the MBL transition, providing new insights into the transition's critical properties.

Findings

The entanglement spectrum distribution approaches a Marchenko-Pastur-like form in the thermal phase.

A correlation length $L_s(h)$ diverges at the MBL transition.

Subleading corrections to entanglement measures are discussed.

Abstract

We study the details of the distribution of the entanglement spectrum (eigenvalues of the reduced density matrix) of a disordered spin chain exhibiting a many-body localization (MBL) transition. In the thermalizing region we identify the evolution under increasing system size of the eigenvalues distribution function, whose thermodynamic limit is close (but possibly different from) the Marchenko-Pastur distribution. From the analysis we extract a correlation length $L_s(h)$ determining the minimum system size to enter the asymptotic region. We find that $L_s(h)$ diverges at the MBL transition. We discuss the nature of the subleading corrections to the entanglement spectrum distribution and to the entanglement entropy.