Thermal equation of state of polarized fermions in one dimension via complex chemical potentials

TL;DR

This paper nonperturbatively computes the thermodynamics of polarized, attractively interacting fermions in one dimension at finite temperature using lattice Monte Carlo methods with complex chemical potentials, providing insights into pairing and spin effects.

Contribution

It introduces a lattice Monte Carlo approach with imaginary chemical potentials to study the equation of state of polarized fermions in 1D, avoiding the sign problem and enabling analysis at strong coupling.

Findings

Results for density, magnetization, susceptibility, and Tan's contact.

Comparison with virial expansion and perturbation theory.

Insights into pairing correlations at various temperatures and spin imbalances.

Abstract

We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on the imaginary side are analytically continued to obtain results on the real axis. We focus on an intermediate- to strong-coupling regime, and cover a wide range of temperatures and spin imbalances.