Fourth cluster and virial coefficients of a unitary Fermi gas for an arbitrary mass ratio

TL;DR

This paper computes the fourth cluster and virial coefficients of a unitary Fermi gas across various mass ratios, revealing complex behaviors near Efimov thresholds and providing analytical results for impurity cases.

Contribution

It introduces an efficient numerical method to calculate higher-order cluster coefficients and extends analytical results to impurity scenarios at infinite mass.

Findings

Fourth cluster coefficients vary significantly near Efimov thresholds.

Fourth virial coefficients are poor indicators of four-body correlations.

Non-monotonic behavior of cluster coefficients in a harmonic trap near specific mass ratios.

Abstract

We calculate the fourth cluster coefficients of the homogeneous unitary spin 1/2 Fermi gas as functions of the internal-state mass ratio, over intervals constrained by the 3- or 4-body Efimov effect. For this we use our 2016 conjecture (validated for equal masses by Hou and Drut in 2020) in a numerically efficient formulation making the sum over angular momentum converge faster, which is crucial at large mass ratio. The mean cluster coefficient, relevant for equal chemical potentials, is not of constant sign and increases rapidly close to the Efimovian thresholds. We also get the fourth virial coefficients, which we find to be very poor indicators of interaction-induced 4-body correlations. We obtain analytically for all $n$ the cluster coefficients of order $n$ + 1 for an infinity-mass impurity fermion, matching the conjecture for $n=3$. Finally, in a harmonic potential, we predict a non-monotonic behavior of the 3 + 1 cluster coefficient with trapping frequency, near mass ratios where this coefficient vanishes in the homogeneous case.