From BCS-Like Superconductivity to Condensation of Local Pairs: A Numerical Study of the Attractive Hubbard Model

We investigate the two-dimensional attractive Hubbard model with quantum Monte Carlo techniques to reveal the crossover from a BCS-type superconductivity in the weak coupling regime to a superconductivity properly described by a Bose--Einstein condensation (BEC) of local, preformed pairs. The crossover from BCS to BEC is particularly well exposed in the temperature dependence of both the spin susceptibility and the double occupancy, as well as by the appearance of a pseudogap in the density of states far above $T_{\rm c}$. These features are also mirrored in the shape of the specific heat peak around $T_{\rm c}$, the separation of the temperature regimes where pair formation and their condensation occurs, and in the transfer of spectral weight from the single-particle excitation branch to a pair band in the normal state.