Distinguishing localization from chaos: challenges in finite-size systems

TL;DR

This paper critically examines the use of certain measures to study many-body localization transitions, highlighting significant finite-size effects that can mislead conclusions about the phase transition and the existence of MBL as a true phase.

Contribution

The paper provides a rigorous analysis showing that commonly used measures are heavily influenced by finite-size effects, challenging recent claims about the nature of the MBL transition.

Findings

Finite-size effects significantly distort measures in MBL studies

Common measures may not reliably indicate the MBL transition

Recent studies might have reached misleading conclusions due to these effects

Abstract

We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models for which rigorous results are available, we find that these measures can be particularly adversely affected by the strong finite-size effects observed in nearly all numerical studies of many-body localization. This severely impacts their utility in probing the transition and the localized phase. In light of this analysis, we argue that a recent study [\v{S}untajs et al., arXiv:1905.06345] of the behavior of the Thouless energy and level repulsion in disordered spin chains likely reaches misleading conclusions, in particular as to the absence of MBL as a true phase of matter.