  Ultracold atomic Fermi gases have been a popular topic of research, with
attention being paid recently to two-dimensional (2D) gases. In this work, we
perform T=0 ab initio diffusion Monte Carlo calculations for a strongly
interacting two-component Fermi gas confined to two dimensions. We first go
over finite-size systems and the connection to the thermodynamic limit. After
that, we illustrate pertinent 2D scattering physics and properties of the wave
function. We then show energy results for the strong-coupling crossover, in
between the Bose-Einstein Condensation (BEC) and Bardeen-Cooper-Schrieffer
(BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to
produce an equation of state, which is used to determine Tan's contact. We
carry out a detailed comparison with other microscopic results. Finally, we
calculate the pairing gap for a range of interaction strengths in the strong
coupling regime, following from variationally optimized many-body wave
functions.
