Absence of Many-Body Localization in a Single Landau Level

TL;DR

This paper investigates many-body localization in a single Landau level and finds no evidence of localization in the thermodynamic limit, showing that extended single-particle states prevent many-body localization.

Contribution

It provides evidence that many-body localization does not occur in a single Landau level due to the presence of extended states, challenging previous assumptions.

Findings

Level spacing ratios indicate a crossover from extended to localized states.

The transition depends strongly on system size and scales to infinite disorder.

Many-body localization is absent in these systems in the thermodynamic limit.

Abstract

The dynamics of the highly excited states of a system projected into a single Landau level are analyzed. An analysis of level spacing ratios for finite size systems shows a clear crossover from extend (GUE) to localized (Poisson) statistics, indicating a many body localization transition. However, the location of this transition depends very strongly on system size, and appears to scale to infinite disorder in the thermodynamic limit. This result does not depend on the properties of the ground state (such as whether the ground state exhibits topological order), as expected for a transition of highly-excited eigenstates. We therefore conclude that many body localization does not exist in these systems. Our results demonstrate that a sub-thermodynamic number of single particle effectively extended states is sufficient to cause all many body states to become extended.