Integer quantum Hall effect of interacting electrons: dynamical scaling and critical conductivity

TL;DR

This study investigates how electron interactions affect the integer quantum Hall effect, revealing dynamical scaling with a critical exponent and showing that key conductance properties remain unchanged by interactions.

Contribution

It provides numerical evidence that electron interactions do not alter the critical conductivity and diffusion exponents at the quantum Hall transition, supporting non-interacting electron models.

Findings

Dynamical scaling with z=1 at the transition

Conductivity remains consistent with non-interacting electrons

Anomalous diffusion exponent unaffected by interactions

Abstract

We report on a study of interaction effects on the polarization of a disordered two-dimensional electron system in a strong magnetic field. Treating the Coulomb interaction within the time-dependent Hartree-Fock approximation we find numerical evidence for dynamical scaling with a dynamical critical exponent z=1 at the integer quantum Hall plateau transition in the lowest Landau level. Within the numerical accuracy of our data the conductivity at the transition and the anomalous diffusion exponent are given by the values for non-interacting electrons, independent of the strength of the interaction.