An Investigation of the Electron Transfer and Repulsive Coulomb Interactions in the One-, Two-, Three-Dimensional Isotropic Hubbard Models I: Eigenfunctions and Eigenvalues

Abstract

In this paper we investigate the Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices with arbitrary values of transfer and on-site repulsion parameters. The method of diagonalization is based on equivalences due to Stevens for number conserving operators and a unitary transformation utilizing permutational symmetries of the problem. We obtained simple analytical formulas for single particle eigenstates and somewhat more involved expression for determinantal multi-electron states. Numerical calculations have been performed which demonstrate the boundaries of the lowest band for various filling 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 Monté Carlo technique in conjunction with particle conservation requirements. Agreement with some well-known limiting cases has been found.