The Second Virial Coefficient of Spin-1/2 Interacting Anyon System

TL;DR

This paper calculates the second virial coefficient of a spin-1/2 anyon gas with a specific repulsive interaction, revealing how it transitions to known limits and removing regularization artifacts.

Contribution

It introduces a method to evaluate the virial coefficient for interacting anyons using propagator regularization and analyzes the behavior as interaction strength varies.

Findings

Cusps disappear in the zero-frequency limit.

Results reduce to noninteracting limit as interaction vanishes.

Method effectively handles regularization of the propagator.

Abstract

Evaluating the propagator by the usual time-sliced manner, we use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form $g/r^2 (g > 0)$. All the cusps for the unpolarized spin-1/2 as well as spinless cases disappear in the $\omega \to 0$ limit, where $\omega$ is a frequency of harmonic oscillator which is introduced as a regularization method. As $g$ approaches to zero, the result reduces to the noninteracting hard-core limit.