Phase diagram of the two-dimensional negative-UHubbard model

Theoretical arguments and numerical calculations are used to discuss the phase diagram of the two-dimensional negative-U Hubbard model. Our results are consistent with (1) a vanishing transition temperature at half-filling but with a ground state having both superconducting and charge-density-wave long-range order, and (2) a Kosterlitz-Thouless transition at a finite temperature into a superconducting state with power-law decay of the pairing correlations away from half-filling.