A new field theoretic method for the virial expansion

TL;DR

This paper introduces a graphical, field-theoretic approach to calculating virial expansion coefficients in quantum systems, successfully computing the third virial coefficient for unitary fermions with high accuracy.

Contribution

It presents a novel graphical method for virial coefficient calculations in quantum field theory, demonstrated by an accurate nonperturbative computation of b3 for unitary fermions.

Findings

Computed b3 = -0.2930, within 0.7% of previous results

Developed a nonperturbative, graphical approach for virial coefficients

Validated the method with a comparison to existing high-precision data

Abstract

We develop a graphical method for computing the virial expansion coefficients for a nonrelativistic quantum field theory. As an example we compute the third virial coefficient b3 for unitary fermions, a nonperturbative system. By calculating several graphs and performing an extrapolation, we arrive at b3 =-0.2930, within 0.7% of a recent computation b3 = -0.29095295 by Liu, Hu and Drummond, which involved summing 10,000 energy levels for three unitary fermions in a harmonic trap.