Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations

TL;DR

This paper develops a virial expansion method to analyze the thermodynamics of a strongly correlated, imbalanced Fermi gas at high temperatures, providing insights into ferromagnetism and equations of state.

Contribution

It extends the virial expansion to imbalanced Fermi gases and estimates the upper bound of the ferromagnetic transition temperature.

Findings

No itinerant ferromagnetism in the repulsive case at high temperatures.

Upper bound for the ferromagnetic transition temperature is below the Fermi temperature.

High-temperature equations of state can guide future thermodynamic measurements.

Abstract

Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin population imbalance. Up to the third order, we calculate the high-temperature free energy of a unitary Fermi gas as a function of spin imbalance, with infinitely large, attractive or repulsive interactions. In the latter repulsive case, we show that there is no itinerant ferromagnetism when quantum virial expansion is applicable. We therefore estimate an upper bound for the ferromagnetic transition temperature $T_{c}$. For a harmonically trapped Fermi gas at unitarity, we find that $(T_{c})_{uppper}<T_{F}$, where $T_{F}$ is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.