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Recent experiments with ultracold fermionic atoms in optical lattices haveprovided a tuneable and clean realization of the attractive Hubbard model(AHM). In view of this, several physical properties may be thoroughly studiedacross the crossover between weak (Bardeen-Cooper-Schrieffer, BCS) and strong(Bose-Einstein condensation, BEC) couplings. Here we report on extensivedeterminant Quantum Monte Carlo (DQMC) studies of the AHM on a square lattice,from which several different quantities have been calculated and should beuseful as a roadmap to experiments. We have obtained a detailed phase diagramfor the critical superconducting temperature, $T_c$, in terms of the bandfilling, $\ave{n}$, and interaction strength, $U$, from which we pinpoint asomewhat wide region $|U|/t \approx 5 \pm 1$ ($t$ is the hopping amplitude) and$\ave{n} \approx 0.79 \pm 0.09$ leading to a maximum $T_c \approx 0.16 t$. Twoadditional temperature scales, namely pairing, $T_p$, and degeneracy, $T_d$,have been highlighted: the former sets the scale for pair formation (believedto be closely related to the scale for the gap of spin excitations incuprates), while the latter sets the scale for dominant quantum effects. OurDQMC data for the distribution of doubly occupied sites, for the momentumdistribution function, and for the quasiparticle weight show distinctivefeatures on both sides of the BCS-BEC crossover, being also suggestive of anunderlying crossover between Fermi- and non-Fermi liquid behaviors.

The 2D attractive Hubbard model and the BCS-BEC crossover