Variational Study of the Two-dimensional Hubbard Model at half-filling

The ground-state properties of the half-filled two-dimensional Hubbard model is systematically investigated by the variational wave function with d-wave supercondcting and anti-ferromagnetic correlations. The enhanced pairing correlation observed in the previous Gutzwiller approximation is found to be strongly suppressed by the doublon-holon and anti-ferromagnetic correlations. In order to check this result, power-Lanczos method is employed to improve the variational wave function. It is found that that pairing is not stable against anti-ferromagnetic long-range order. Possible models for the theory Gossamer superconductivity will be discussed in this paper.