Absence of Many-Body Localization in a Single Landau Level

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.

References in corpus (5)

• Many-body localization edge in the random-field Heisenberg chain
• Critical exponent for the quantum Hall transition
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Marginal Anderson localization and many body delocalization
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids

Cited by in corpus (1)

• Integer quantum Hall transition in a $\text{fraction}$ of a Landau level