Quantum Hall conductivity in the presence of interactions

TL;DR

This paper demonstrates that the Hall conductivity in quantum Hall systems remains equal to the averaged Landau level filling fraction, regardless of interaction strength, applicable to both integer and fractional cases.

Contribution

It establishes a universal relation between Hall conductivity and Landau level filling fraction that holds even with arbitrary electron interactions.

Findings

Hall conductivity equals the averaged Landau level filling fraction.

The result applies to both integer and fractional quantum Hall effects.

Interaction strength does not alter the fundamental conductivity relation.

Abstract

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over the ground state of the system. This conclusion remains valid for both integer and fractional quantum Hall effect.