Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons

TL;DR

This paper analyzes the statistical interparticle potential of non-Abelian Chern-Simons particles, revealing a phase diagram with quasi-bosonic, quasi-fermionic, and bosonic-like regions, and computes the second virial coefficient matching known results.

Contribution

It introduces a detailed study of the statistical potential for non-Abelian anyons, extending the understanding from Abelian cases and providing a phase diagram based on Chern-Simons coupling and isospin.

Findings

Behavior of the potential depends on Chern-Simons coupling and isospin.

Phase diagram with distinct quasi-bosonic, quasi-fermionic, and bosonic-like regions.

Second virial coefficient matches existing literature results.

Abstract

We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical potential depends on the Chern- Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in literature.