Spin Polarized Non-Relativistic Fermions in 1+1 Dimensions

TL;DR

This study uses Monte Carlo simulations to analyze spin polarized non-relativistic fermions in 1+1 dimensions, revealing a lack of sign problem and enabling exploration of previously inaccessible polarization regimes.

Contribution

It demonstrates that the action for these fermions has no significant sign problem across relevant polarizations, allowing non-perturbative studies of attractive spin polarized fermions.

Findings

No significant sign problem in the studied parameter region.

Verification of some previous results using alternative methods.

Observation of deviations from prior results at higher polarizations.

Abstract

We study by Monte Carlo methods the thermodynamics of a spin polarized gas of non-relativistic fermions in 1+1 dimensions. The main result of this work is that our action suffers no significant sign problem for any spin polarization in the region relevant for dilute degenerate fermi gases. This lack of sign problem allows us to study attractive spin polarized fermions non-perturbatively at spin polarizations not previously explored. For some parameters values we verify results previously obtained by methods which include an uncontrolled step like complex Langevin and/or analytical continuation from imaginary chemical potential. For others, larger values of the polarization, we deviate from these previous results.