Evidence for a Pseudogap Above the Critical Temperature in the Attractive Hubbard Model

We explore the effect of fluctuations for $T \geq T_c$ in the 2-D negative Hubbard model within the framework of the selfconsistent T-matrix formalism, which goes beyond the BCS approximation and includes pair fluctuations. We enter the regime where correlations are important, namely, $U/t = -4.0$, where $t$ denotes the hopping matrix element between nearest neighboors and $U$ is the strength of the on-site interaction. Our results include: 1) In comparison to the free case, the distribution function, $n({\bf k})$, reveals considerable renormalization. This fact makes us conclude that the Fermi surface is blurred for correlated electron systems; 2) There is a pseudogap in the density of states, $N(\omega)$, around the chemical potential, $\mu$; and 3) The real part of the T-matrix, at zero frequency and zero momentum, vs $T/t$ shows a divergence at a particular temperature. This last result shows that more approximate T-matrix calculations, extended to $T~=~0$ are meaningless.