Many-Body Localization and Level Repulsion

TL;DR

This paper investigates how disorder affects level repulsion in many-body localized quantum systems, showing most eigenstates can be approximated and that rare resonances are exponentially suppressed in the localized phase.

Contribution

It provides a perturbative analysis of level repulsion effects in many-body localized phases, classifies rare resonances, and discusses conditions for transition to thermal phases.

Findings

Most eigenstates are accurately approximated, including rare resonances.

Rare resonances are exponentially rare and require fine tuning.

No rare thermal eigenstates exist in a fully localized phase.

Abstract

Insertion of disorder in thermal interacting quantum systems decreases the amount of level repulsion and can turn them into many body localized phases. In this paper we use the many body picture to perturbatively study the effect of level repulsion in the localized phase. We find that most eigenstates can be described accurately in an approximate way, including many with rare resonances. A classification of the rare resonances shows that most types are exponentially rare and requires exponential fine tuning in an approximate description. The classification confirms that no rare thermal eigenstates can exist in a fully localized phase and we argue that all types of resonances need to become common if a continuous transition into a thermal phase should occur.