Virial expansion for the Tan contact and Beth-Uhlenbeck formula from 2D SO(2,1) anomalies

TL;DR

This paper connects 2D $SO(2,1)$ conformal anomalies to the virial expansion, deriving the Beth-Uhlenbeck formula and a virial expansion for the Tan contact using path-integral methods, with discussions on extending these results.

Contribution

It introduces a novel approach linking conformal anomalies to virial expansions and derives new formulas for the second virial coefficient and Tan contact in 2D systems.

Findings

Derived the Beth-Uhlenbeck formula for $\, ext{delta}b_2$

Established a virial expansion for the Tan contact

Discussed potential extensions to higher virial orders

Abstract

The relationship between 2D $SO(2,1)$ conformal anomalies in nonrelativistic systems and the virial expansion is explored using recently developed path-integral methods. In the process, the Beth-Uhlenbeck formula for the shift of the second virial coefficient $\delta b_2$ is obtained, as well as a virial expansion for the Tan contact. A possible extension of these techniques for higher orders in the virial expansion is discussed.