Quantum Monte Carlo Study of Strongly Interacting Fermi Gases in Two Dimensions: BCS-BEC Crossover, Spin-orbit Coupling, and Dynamical Response Functions*

We describe recent advances in
auxiliary-field quantum Monte Carlo techniques, which enable
calculations on large lattices to reliably compute ground-state and excited-state
properties in the thermodynamic limit. Exact calculations are performed on the two-dimensional strongly interacting, unpolarized, uniform Fermi gas with a zero-range
attractive interaction. An equation of state is
obtained, with a parametrization provided, which can serve as a
benchmark and allow accurate comparisons with experiments. The
pressure, contact parameter, and condensate fraction are determined
systematically vs. the interaction strength. Rashba spin-orbit coupling is then
included to examine its interplay with superfluidity and the resulting
pairing and spin structures and correlations. The imaginary-time propagation of Slater determinants is used to compute the pairing gap in the two-dimensional Fermi gas. The spectral functions, and the density and spin structure factors are then obtained using analytic continuation to provide unique tools to visualize the BEC-BCS crossover. We will also discuss briefly calculations in optical lattice systems and comment on the prospect for precision calculations in spin-imbalanced systems.