The crossover from BEC to BCS in the interacting 2D Fermi gas

The physics of the two-species Fermi gas with an attractive contact interaction in two spatial dimensions (2D) is different from the 3D system in that there is a two-particle bound state for any strength of the interaction. We investigate the thermodynamics of the strongly interacting 2D Fermi system in the crossover between the Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) limits using finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods in the canonical ensemble. In particular, we study the superfluid phase transition and the possible existence and extent of a pseudogap regime, in which signatures of pairing correlations survive above the critical temperature. To this end, we calculate the temperature dependence of the condensate fraction and of a model-independent energy staggering pairing gap. We also calculate the temperature dependence of the contact, a fundamental property of quantum many-body systems with short-range correlations which measures the pair correlation at short distances. Our AFMC simulations are carried out on a discrete lattice and extrapolated to the continuum limit.