The possibility of superconductivity in the ground state of the two-dimensional Hubbard model was investigated by means of the variational Monte Carlo method. With slight hole doping on the 6 ×6 and 10 ×10 lattices, a clear minimum was obtained on the curve of the total energy versus the amplitude of the d -wave gap function for large on-site Coulomb energies. Superconducting pair correlations were observed to be well developed. The-next-nearest-neighbor transfer was found to appreciably affect the minimum depth.
We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp(
−S)-type where
S is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The
d-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the
d-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.
We reexamine the possibility of d-wave superconductivity in the hole-doped two-dimensional Hubbard model. In terms of the gauge field description of the spin fluctuations, we show that d-wave superconductivity is unstable in the perturbative region with respect to the on-site Coulomb repulsion, U. Whereas in the region where d-wave superconductivity is possible, there is a strong constraint on the gap of superconductivity. Analysis of the localized spin moments suggests that there is another d-wave (d_{x^2-y^2}-wave) pairing due to the short-range antiferromagnetic correlation.