Virial expansion with Feynman diagrams

TL;DR

This paper introduces an analytic field theoretic approach to calculate the second and third virial coefficients for interacting fermions, providing explicit expressions and confirming previous numerical results across the BEC-BCS crossover.

Contribution

It develops a mostly analytic method using Feynman diagrams to compute virial coefficients, including a closed-form expression for b3 in terms of T-matrices.

Findings

Derived a closed expression for b3 in terms of 2 and 3-body T-matrices.

Numerically confirmed the value of b3 at unitarity and across the BEC-BCS crossover.

Validated the method by recovering previous numerical results.

Abstract

We present a field theoretic method for the calculation of the second and third virial coefficients b2 and b3 of 2-species fermions interacting via a contact interaction. The method is mostly analytic. We find a closed expression for b3 in terms of the 2 and 3-body T-matrices. We recover numerically, at unitarity, and also in the whole BEC-BCS crossover, previous numerical results for the third virial coefficient b3.