Distinguishing localization from chaos: Challenges in finite-size systems

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 discuss a recent study (?untajs et al., 2020) of the behaviour of the Thouless energy and level repulsion in disordered spin

Automated summary

Through analyzing the measures in the study of many-body localization, it is found that their utility in probing the transition and the localized phase can be severely impacted due to strong finite-size effects.