Improved wave functions for Hubbard model: Superconductivity and Mott transition

We extend the doublon-holon binding wave function, which was recently often used to consider Mott transitions and dx2-y2-wave superconductivity, for the half-filled-band Hubbard model on square lattices with the diagonal hopping t′. We introduce two new features: (1) In the doublon-holon binding factor, more accurate configuration correlations are included. (2) The band renormalization effect owing to the electron correlation is introduced within the third-neighbor hopping, including the anisotropy between x- and y-directions in the nearest-neighbor hopping. Using an optimization variational Monte Carlo technique, we draw some definite answers to the topics concerning the above features.