  We describe the treatment of Rashba spin-orbit coupling (SOC) in interacting
many-fermion systems within the auxiliary-field quantum Monte Carlo framework,
and present a set of illustrative results. These include numerically exact
calculations on the ground-state properties of the spin-balanced, attractive
two-dimensional Fermi gas, as well as a study of a tight-binding Hamiltonian
with repulsive interaction. These systems are formally connected via the
Hubbard Hamiltonian with SOC, but cover different physics ranging from
superfluidity and triplet pairing to SOC in real materials in the presence of
strong interactions in localized orbitals. We carry out detailed benchmark
studies of the method in the latter case when an approximation is needed to
control the sign problem for repulsive Coulomb interactions. The methods
presented here provide an approach for predictive computations in materials to
study the interplay of SOC and strong correlation.
