Virial coefficients of 1D and 2D Fermi gases by stochastic methods and a semiclassical lattice approximation

TL;DR

This paper investigates the interaction effects on virial coefficients of 1D and 2D Fermi gases using stochastic methods and a semiclassical approximation, providing new insights into their behavior at different coupling strengths.

Contribution

It introduces non-perturbative stochastic techniques to compute high-order virial coefficients and compares these results with a semiclassical lattice approximation, advancing understanding of Fermi gas interactions.

Findings

High-order virial coefficients computed for 1D Fermi gases.

Semiclassical lattice approximation closely matches numerical results.

Estimation of the virial expansion's radius of convergence.

Abstract

We map out the interaction effects on the first six virial coefficients of one-dimensional Fermi gases with zero-range attractive and repulsive interactions, and the first four virial coefficients of the two-dimensional analog with attractive interactions. To that end, we use two non-perturbative stochastic methods: projection by complex stochastic quantization, which allows us to determine high-order coefficients at weak coupling and estimate the radius of convergence of the virial expansion; and a path-integral representation of the virial coefficients. To complement our numerical calculations, we present leading-order results in a semiclassical lattice approximation, which we find to be surprisingly close to the expected answers.