Fourth- and fifth-order virial expansion of harmonically trapped fermions at unitarity

TL;DR

This paper extends the virial expansion to fifth order for harmonically trapped unitary fermions, providing new coefficients and thermodynamic predictions that align with previous Monte Carlo results and improve understanding of trapped quantum gases.

Contribution

It introduces a generalized algebra approach to compute higher-order virial coefficients for trapped fermions, advancing theoretical tools for quantum many-body systems.

Findings

Calculated fourth- and fifth-order virial coefficients for trapped fermions.

Results agree with previous Monte Carlo calculations at fourth order.

Provided thermodynamic quantities like compressibility and spin susceptibility.

Abstract

By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an isotropic harmonic potential. We present results for said coefficients as a function of trapping frequency (or, equivalently, temperature), which compare favorably with previous Monte Carlo calculations (available only at fourth order) as well as with our previous estimates in the untrapped limit (high temperature, low frequency). We use our estimates of the virial expansion, together with resummation techniques, to calculate the compressibility and spin susceptibility.