Virial Expansions, Exclusion Statistics, and the Fractional Quantum Hall Effect

TL;DR

This paper investigates virial expansions for interacting electrons in the fractional quantum Hall regime, deriving analytic results at low temperatures and analyzing the breakdown of exclusion statistics at higher temperatures.

Contribution

It provides analytic expressions for virial coefficients in the fractional quantum Hall effect and examines the limits of exclusion statistics descriptions.

Findings

Virial coefficients match non-interacting systems at high temperatures.

Exclusion statistics description fails above a small fraction of the gap temperature.

Numerical analysis of the first five virial coefficients across temperature regimes.

Abstract

We report on a study of virial expansions for interacting electrons in the lowest Landau level of a two-dimensional electron gas. For hard-core-model interactions, we derive analytic results valid at low temperatures and filling factors smaller than 1/3 and comment on their relationship with virial expansions for exclusion statistics models. In the high temperature limit the virial coefficients reduce to those for a non-interacting electron system. For the first five virial coefficients, the crossover between low and high temperature limits has been studied numerically by using partition functions obtained from small system exact diagonalization calculations. Our results show that the exclusion statistics description of fractional Hall thermodynamics breaks down when the temperature exceeds a small fraction of the gap temperature.