Precision thermodynamics of the strongly interacting Fermi gas in two dimensions

The two-species cold atomic Fermi gas with attractive short-range interactions in two spatial dimensions undergoes a Bardeen-Cooper-Schrieffer (BCS) to a Bose-Einstein Condensate (BEC) crossover as a function of $\ln (k_F a)$, where $a$ is the scattering length. However, the nature of this crossover in the strong coupling regime $\ln(k_F a) \sim 1$ remains poorly understood. In this work we use canonical-ensemble auxiliary-field quantum Monte Carlo methods on discrete lattices to calculate several thermodynamical quantities in the strongly interacting regime, and eliminate systematic errors by extrapolating to continuous time and taking the continuum limit. In particular, we present results for the condensate fraction, spin susceptibility, contact, energy equation of state, and the free energy staggering gap. We identify signatures of a pseudogap regime, in which pairing correlations survive above the critical temperature for superfluidity, in the spin susceptibility and in the free energy staggering gap. These results can be used as a benchmark for future experiments.