An investigation of the electron transfer and repulsive Coulomb interactions in the one-, two-, three-dimensional isotropic Hubbard models - II: Extension to a Wannier and higher angular momentum basis

摘要

In the previous paper we have investigated the isotropic Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices. The method involved the determination of the one-electron energies and eigenfunctions of the transfer interaction, the latter being utilised to form determinantal eigenfunctions for the many-electron system as a whole. In this paper we have examined the consequences of using an atomic basis by introducing; Wannier functions and studied physical consequences of this more exact approach. To reduce the transformed two-body interaction to manageable form we have used the rotational properties of individual atomic orbitals incorporating them via irreducible tensorial methods. We find that, although additional components due to Wannier "tails" are small they may modify the nearest neighbor transfer terms significantly and also introduce next-nearest and next-next nearest neighbor transfer interactions. We have also investigated the effect of using atomic orbitals with a higher angular momentum on each site. Both p-orbitals and d-orbitals have been studied and the broad conclusion is that the corresponding Hubbard model reduces to a series of S-like orbital models, one for each component, m, of the degenerate set on each site. The transfer interaction in each case becomes, in general, m dependent, each m component being effectively decoupled from others. [References: 15]