Many-body localization in Landau-level subbands

Abstract

© 2019 American Physical Society. We explore the problem of localization in topological and nontopological 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 pointlike impurities. We perform numerical exact diagonalization on a torus geometry and use the mean level spacing ratio (r) 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 nontopological subbands, in contrast, 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, continuum setting for the study of the many-body localization transition in one and two dimensions.