Many-body localization in Landau level subbands

TL;DR

This paper investigates many-body localization in Landau level subbands, revealing ergodicity breaking in non-topological cases but not in topological ones, using numerical methods in continuum models.

Contribution

It provides the first continuum study of many-body localization in Landau level subbands, distinguishing behaviors between topological and non-topological cases.

Findings

No ergodicity breaking in topological subbands.

Evidence of ergodicity breaking transition in non-topological subbands.

Indications of similar behavior in 2D thermodynamic limit.

Abstract

We explore the problem of localization in topological and non-topological nearly-flat subbands derived from the lowest Landau level, in the presence of quenched disorder and short-range interactions. We consider two models: a suitably engineered periodic potential, and randomly distributed point-like impurities. We perform numerical exact diagonalization on a torus geometry and use the mean level spacing ratio $\langle r \rangle$ as a diagnostic of ergodicity. For topological subbands, we find there is no ergodicity breaking in both the one and two dimensional thermodynamic limits. For non-topological subbands, in constrast, we find evidence of an ergodicity breaking transition at finite disorder strength in the one-dimensional thermodynamic limit. Intriguingly, indications of similar behavior in the two-dimensional thermodynamic limit are found, as well. This constitutes a novel, $\textit{continuum}$ setting for the study of the many-body localization transition in one and two dimensions.