An investigation of the electron transfer and repulsive Coulomb interactions in the one, two-, three-dimensional isotropic Hubbard models - I: Eigenfunctions and eigenvalues

In this paper we investigate the Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices with arbitrary val ues of transfer and on-site repulsion parameters. The method of diagonaliza tion is based on equivalences due to Stevens for number conserving operator s and a unitary transformation utilizing permutational symmetries of the pr oblem. We obtained simple analytical formulas for single particle eigenstat es and somewhat more involved expression for determinantal multi-electron s tates. Numerical calculations have been performed which demonstrate the bou ndaries of the lowest band for various filing factors using examples in one - and two-dimensions. The states within the band have also been identified and degeneracies evaluated numerically. These computations were based on a Monte Carlo technique in conjunction with particle conservation requirement s. Agreement with some well-known limiting cases has been found.