  The BCS-BEC crossover within the two-dimensional attractive Hubbard model is
studied by using the Cellular Dynamical Mean-Field Theory both in the normal
and superconducting ground states. Short-range spatial correlations
incorporated in this theory remove the normal-state quasiparticle peak and the
first-order transition found in the Dynamical Mean-Field Theory, rendering the
normal state crossover smooth. For $U$ smaller than the bandwidth, pairing is
driven by the potential energy, while in the opposite case it is driven by the
kinetic energy, resembling a recent optical conductivity experiment in
cuprates. Phase coherence leads to the appearance of a collective Bogoliubov
mode in the density-density correlation function and to the sharpening of the
spectral function.
