Many-body localization in Landau level subbands

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 $⟨r⟩$ 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 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, $\text{continuum}$ setting for the study of the many-body localization transition in one and two dimensions.

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• Flat-band many-body localization and ergodicity breaking in the Creutz ladder
• Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model
• Topology and many-body localization
• Localization and interactions in topological and non-topological bands in two dimensions
• Analog Circuit-QED Simulator of Quantum Spin Dynamics Through the Extended Bose-Hubbard Model