Energy dependence of localization with interactions and disorder: The generalized inverse participation ratio of an ensemble of two-site Anderson-Hubbard systems

TL;DR

This paper investigates how interactions and disorder influence localization in small Anderson-Hubbard systems, revealing persistent non-analytic features in the density of states linked to localization suppression and many-body effects.

Contribution

It extends the understanding of localization phenomena by analyzing the impact of Hubbard interactions on the density of states and localization in disordered small systems.

Findings

Persistence of a cusp in the density of states with interactions

Sharp suppression of localization near the cusp

Connection to many-body localization phenomena

Abstract

After Anderson's prediction of disorder-induced insulating behavior, extensive work found no singularities in the density of states of localized systems. However, Johri and Bhatt recently uncovered the existence of a non-analyticity in the density of states near the band edge of non-interacting systems with bounded disorder, in an energy range outside that captured by previous work. Moreover, this feature marks the boundary of an energy range in which the localization is sharply suppressed. Given strong current interest in the effect of interactions on disordered systems, we explore here the effect of a Hubbard $U$ interaction on this behavior. We find that in ensembles of small systems a cusp in the density of states persists and continues to be associated with a sharp suppression of the localization. We explore the origins of this behavior and discuss its connection with many-body localization.