Topology and many-body localization

TL;DR

This paper investigates the possibility of many-body localization in two-dimensional quantum Hall systems, showing that MBL is unlikely in a single Landau level with short-range disorder, but topology influences localization and dynamics.

Contribution

It provides numerical evidence that topology significantly affects many-body localization and slow dynamics in quantum Hall systems, contrasting topological and nontopological bands.

Findings

MBL is not achievable in a single Landau level with short-range disorder in the thermodynamic limit.

Topology impacts the feasibility of many-body localization and influences slow dynamics.

Topological bands exhibit different localization behavior compared to nontopological bands.

Abstract

We discuss the problem of localization in two dimensional electron systems in the quantum Hall (single Landau level) regime. After briefly summarizing the well-studied problem of Anderson localization in the non-interacting case, we concentrate on the problem of disorder induced many-body localization (MBL) in the presence of electron-electron interactions using numerical exact diagonalization and eigenvalue spacing statistics as a function of system size. We provide evidence showing that MBL is not attainable in a single Landau level with short range (white noise) disorder in the thermodynamic limit. We then study the interplay of topology and localization, by contrasting the behavior of topological and nontopological subbands arising from a single Landau level in two models - (i) a pair of extremely flat Hofstadter bands with an optimally chosen periodic potential, and (ii) a Landau level with a split-off nontopological impurity band. Both models provide convincing evidence for the strong effect of topology on the feasibility of many-body localization as well as slow dynamics starting from a nonequilibrium state with charge imbalance.