Haldane exclusion statistics and second virial coefficient

TL;DR

This paper demonstrates that Haldane's exclusion statistics parameter g, when extended to infinite-dimensional spaces, equals the high-temperature limit of the second virial coefficient, linking it to exchange statistics.

Contribution

It establishes a direct connection between Haldane's exclusion statistics and the second virial coefficient, providing explicit calculations for anyons and Luttinger model quasiparticles.

Findings

g equals the high-temperature limit of the second virial coefficient

g is non-trivial and determined by exchange statistics parameter α

g for Luttinger quasiparticles equals α

Abstract

We show that Haldanes new definition of statistics, when generalised to infinite dimensional Hilbert spaces, is equal to the high temperature limit of the second virial coefficient. We thus show that this exclusion statistics parameter, g , of anyons is non-trivial and is completely determined by its exchange statistics parameter $\alpha$. We also compute g for quasiparticles in the Luttinger model and show that it is equal to $\alpha$.