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We describe the treatment of Rashba spin-orbit coupling (SOC) in interactingmany-fermion systems within the auxiliary-field quantum Monte Carlo framework,and present a set of illustrative results. These include numerically exactcalculations on the ground-state properties of the spin-balanced, attractivetwo-dimensional Fermi gas, as well as a study of a tight-binding Hamiltonianwith repulsive interaction. These systems are formally connected via theHubbard Hamiltonian with SOC, but cover different physics ranging fromsuperfluidity and triplet pairing to SOC in real materials in the presence ofstrong interactions in localized orbitals. We carry out detailed benchmarkstudies of the method in the latter case when an approximation is needed tocontrol the sign problem for repulsive Coulomb interactions. The methodspresented here provide an approach for predictive computations in materials tostudy the interplay of SOC and strong correlation.

Accurate computations of Rashba spin-orbit coupling in interacting systems: from the Fermi gas to real materials