title: Coulomb matrix elements in multi-orbital Hubbard models.
abstract: Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a d-shell and an f-shell and all point groups with up to 16 elements (Oh, O, Td, Th, D6h, and D4h). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order corrections to the spherical approximation.
authors.affiliation: Institut für Physik, BTU Cottbus-Senftenberg, PO Box 101344, 03013 Cottbus, Germany.
authors.forename: Jörg
authors.initials: J
authors.lastname: Bünemann
authors.forename: Florian
authors.initials: F
authors.lastname: Gebhard