Second Virial Coefficient of Anyons without Hard Core

TL;DR

This paper calculates the second virial coefficient for a new class of anyons that do not obey the traditional hard-core boundary condition, revealing novel behaviors and a new cusp at the fermionic point.

Contribution

It introduces a method to compute the virial coefficient for non-hard-core anyons using self-adjoint extension and renormalization, highlighting new physical phenomena.

Findings

Disappearance of the bosonic cusp in non-hard-core anyons

Emergence of a new cusp at the fermionic point

Relevance of scale-invariant limits in high-temperature regimes

Abstract

We calculate the second virial coefficient of anyons whose wave function does not vanish at coincidence points. This kind of anyons appear naturally when one generalizes the hard-core boundary condition according to self-adjoint extension method in quantum mechanics, and also when anyons are treated field theoretically by applying renormalization procedure to nonrelativistic Chern-Simons field theory. For the anyons which do not satisfy hard-core boundary condition, it is argued that the other scale-invariant limit is more relevant in high-temperature limit where virial expansion is useful. Furthermore, the cusp existing at the bosonic point for hard-core anyons disappears in all the other cases; instead it is shown that a new cusp is generated at the fermionic point. A physical explanation is given.