Precision auxiliary-field quantum Monte Carlo computations of Rashba spin-orbit coupling in interacting many-body systems

We describe the treatment of Rashba spin-orbit coupling (SOC) in interacting many-fermion systems within the auxiliary-field quantum Monte Carlo (AFQMC) framework, and present a set of illustrative results. We show that this technique can be applied to a wide range of systems, including the Fermi gas in the continuum and the lattice, with attractive or repulsive interactions. In the unpolarized, attractive case our results provide a numerically exact description of the ground-state of the Fermi gas in the continuum [1], and the lattice [2]. For the repulsive case a constraint is applied and we perform a set of benchmark calculations that achieve similar accuracy to calculations without SOC [3]. These developments enable high-precision AFQMC simulations of many of the novel Hamiltonians currently being engineered in ultra-cold atoms, and provide a general approach for predictive computations in models and materials to study the interplay of SOC and strong correlation. In addition to establishing a new set of benchmarks, this technique offers quantitative numerical insight to guide the search for topological phases.

[1] Phys. Rev. Lett. 117, 040401 (2016)

[2] arXiv:1707.02994

[3] arXiv:1710.00887