Effect of Landau Level Mixing on Braiding Statistics

TL;DR

This paper investigates how Landau level mixing influences the braiding statistics of quasiparticles in quantum Hall states, finding that nonabelian properties are robust against such effects, with only minor perturbations to abelian phases.

Contribution

It demonstrates that nonabelian braiding statistics are unaffected by Landau level mixing, ensuring their stability for quantum computation applications.

Findings

Nonabelian statistics remain unchanged to exponential accuracy.

Path-dependent phases perturb abelian parts of the statistics.

Landau level mixing has negligible impact on nonabelian properties.

Abstract

We examine the effect of Landau level mixing on the braiding statistics of quasiparticles of abelian and nonabelian quantum Hall states. While path dependent geometric phases can perturb the abelian part of the statistics, we find that the nonabelian properties remain unchanged to an accuracy that is exponentially small in the distance between quasiparticles.