Polarized fermions in one dimension: density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion

TL;DR

This paper investigates the density and polarization of one-dimensional polarized fermions at finite temperature using complex Langevin, perturbation theory, and virial expansion, providing a benchmark for higher-dimensional studies.

Contribution

It introduces a comparative analysis of multiple methods to study 1D polarized fermions, validating complex Langevin against perturbation and virial expansion techniques.

Findings

Good agreement between methods in studied regimes

Complex Langevin effectively overcomes the sign problem in 1D

Results support the validity of different approaches for 1D fermion systems

Abstract

We calculate the finite-temperature density and polarization equations of state of one-dimensional fermions with a zero-range interaction, considering both attractive and repulsive regimes. In the path-integral formulation of the grand-canonical ensemble, a finite chemical potential asymmetry makes these systems intractable for standard Monte Carlo approaches due to the sign problem. Although the latter can be removed in one spatial dimension, we consider the one-dimensional situation in the present work to provide an efficient test for studies of the higher-dimensional counterparts. To overcome the sign problem, we use the complex Langevin approach, which we compare here with other approaches: imaginary-polarization studies, third-order perturbation theory, and the third-order virial expansion. We find very good qualitative and quantitative agreement across all methods in the regimes studied, which supports their validity.