Pairing and spin gap in the normal state of short coherence length superconductors

We study the normal state of the 2D attractive Hubbard model using quantum Monte Carlo simulations. We show that singlet pairing correlations develop above ${\mathit{T}}_{\mathit{c}}$, and the normal state of a short coherence length superconductor deviates from a canonical Fermi liquid. In the intermediate U regime, the spin susceptibility ${\mathrm{\chi }}_{\mathit{s}}$ is strongly temperature dependent, and the low-frequency spectral weight, as measured by the NMR relaxation rate 1/${\mathit{T}}_1$T, is shown to track ${\mathrm{\chi }}_{\mathit{s}}$. This provides a simple, qualitative explanation for the spin-gap behavior observed in several high-${\mathit{T}}_{\mathit{c}}$ systems.