Finite-size scaling with respect to interaction and disorder strength at the many-body localization transition

TL;DR

This paper investigates how both interaction and disorder influence the many-body localization transition in a spin chain, introducing a finite-size scaling approach with a new critical exponent to describe their combined effects.

Contribution

It extends previous studies by incorporating interaction dependence into the finite-size scaling analysis of the MBL transition using level statistics.

Findings

The transition depends on a ratio involving disorder strength and interaction raised to a new critical exponent.

An extra critical exponent is introduced to capture the nontrivial interaction dependence.

The study provides a refined understanding of the interplay between disorder and interaction in MBL.

Abstract

We present a finite-size scaling for both interaction and disorder strengths in the critical regime of the many-body localization (MBL) transition for a spin-1/2 XXZ spin chain with a random field by studying level statistics. We show how the dynamical transition from the thermal to MBL phase depends on interaction together with disorder by evaluating the ratio of adjacent level spacings, and thus, extend previous studies in which interaction coupling is fixed. We introduce an extra critical exponent in order to describe the nontrivial interaction dependence of the MBL transition. It is characterized by the ratio of the disorder strength to the power of the interaction coupling with respect to the extra critical exponent and not by the simple ratio between them.