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.
Highlights
Coupled dilute Fermi gases are rich systems which stand at the crossroads of various fields of physics
We study using Monte Carlo methods the physics of a finite density of fermions in one spatial dimension with nonzero spin polarization; here a sign problem exists
We find that the sign problem is extremely mild for a vast range of parameters which correspond to densities small compared to the lattice cutoff scale, which are the relevant parameters for the continuum limit
Summary
Coupled dilute Fermi gases are rich systems which stand at the crossroads of various fields of physics. In the realm of nuclear physics, it is believed that the properties of dilute Fermi gases with large scattering lengths are related to the properties of neutron rich matter at the edge of a neutron star [1]. In the atomic physics community, dilute fermi gases at unitarity have been studied to in the context of the BEC-BCS crossover [4]. Spin polarizing these gases adds a layer of richness to observable phenomena. High magnetic fields in neutron stars can destroy S-wave pairing in neutron matter through spin polarization, which has observable consequences on spectroscopic data gathered from rapidly rotating neutron stars [8]
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