  Standard lattice formulations of non-relativistic Fermi gases with two spin
components suffer from a sign problem in the cases of repulsive contact
interactions and attractive contact interactions with spin imbalance. We
discuss the nature of this sign problem and the applicability of stochastic
quantisation with complex Langevin evolution in both cases. For repulsive
interactions, we find that the results converge, using adaptive step size
scaling and a Gaussian regulator to modify the lattice action. We present
results on density profiles and correlations of a harmonically trapped system
in one spatial dimension.
