Absence of many-body mobility edges

TL;DR

The paper argues that many-body mobility edges are unlikely because local ergodic fluctuations can cause global delocalization, suggesting that true many-body localization requires models localized at all energies.

Contribution

It presents a theoretical argument against the existence of many-body mobility edges and supports it with numerical evidence challenging previous reports.

Findings

Mobility edges are likely finite-size effects.

Localized phases at all energies are necessary for true many-body localization.

Local ergodic fluctuations can induce delocalization in supposedly localized phases.

Abstract

Localization transitions as a function of temperature require a many-body mobility edge in energy, separating localized from ergodic states. We argue that this scenario is inconsistent because local fluctuations into the ergodic phase within the supposedly localized phase can serve as mobile bubbles that induce global delocalization. Such fluctuations inevitably appear with a low but finite density anywhere in any typical state. We conclude that the only possibility for many-body localization to occur are lattice models that are localized at all energies. Building on a close analogy with a model of assisted two-particle hopping, where interactions induce delocalization, we argue why hot bubbles are mobile and do not localize upon diluting their energy. Numerical tests of our scenario show that previously reported mobility edges cannot be distinguished from finite-size effects.