Pressure, compressibility, and contact of the two-dimensional attractive Fermi gas

TL;DR

This paper uses ab initio lattice methods to compute the thermodynamics of a 2D attractive Fermi gas, providing detailed results for density, pressure, compressibility, and Tan's contact across various temperatures and couplings.

Contribution

It offers the first ab initio calculations of 2D Fermi gas thermodynamics, comparing results with Luttinger-Ward theory and virial expansions, highlighting quantitative differences in the strongly coupled regime.

Findings

Density equation of state differs from Luttinger-Ward in strong coupling

Results agree with virial expansion at low fugacity

Provides detailed thermodynamic data across temperature and coupling ranges

Abstract

Using ab initio lattice methods, we calculate the finite temperature thermodynamics of homogeneous two-dimensional spin-1/2 fermions with attractive short-range interactions. We present results for the density, pressure, compressibility, and quantum anomaly (i.e. Tan's contact) for a wide range of temperatures and coupling strengths, focusing on the unpolarized case. Within our statistical and systematic uncertainties, our prediction for the density equation of state differs quantitatively from the prediction by Luttinger-Ward theory in the strongly coupled region of parameter space, but otherwise agrees well with it. We also compare our calculations with the second- and third-order virial expansion, with which they are in excellent agreement in the low-fugacity regime.