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

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.