  We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS)
superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi
gas at T=0 using the fixed-node diffusion Monte Carlo method. We calculate the
equation of state and the gap parameter as a function of the interaction
strength, observing large deviations compared to mean-field predictions. In the
BEC regime our results show the important role of dimer-dimer and atom-dimer
interaction effects that are completely neglected in the mean-field picture.
Results on Tan's contact parameter associated with short-range physics are also
reported along the BCS-BEC crossover.
