Interactions, Localization, and the Integer Quantum Hall Effect

TL;DR

This study uses numerical methods to examine how Coulomb interactions affect electron localization in the quantum Hall regime, finding that interactions do not significantly alter localization properties.

Contribution

It demonstrates that Coulomb interactions, modeled via Hartree-Fock approximation, do not impact localization in the integer quantum Hall effect.

Findings

Localization properties are unaffected by interactions.

Energy level spacings near the Fermi level are enhanced.

Thouless numbers are similar for interacting and non-interacting electrons.

Abstract

We report on numerical studies of the influence of Coulomb interactions on localization of electronic wavefunctions in a strong magnetic field. Interactions are treated in the Hartree-Fock approximation. Localization properties are studied both by evaluating participation ratios of Hartree-Fock eigenfunctions and by studying the boundary-condition dependence of Hartree-Fock eigenvalues. We find that localization properties are independent of interactions. Typical energy level spacings near the Fermi level and the sensitivity of those energy levels to boundary condition show similar large enhancements so that the Thouless numbers of the Hartree-Fock eigenvalues are similar to those of non-interacting electrons.