Effect of Orbital Degeneracy on the Anderson Model of a Localized Moment in a Metal

Abstract

As conventionally written, the localized-center portion of the Anderson Hamiltonian suffers from the defect of lack of rotational invariance in real space (and possibly spin space also) when describing a center with ($2l+1$) degenerate spatial orbitals. A simple modification is suggested which restores the rotational invariance in both spaces. The eigenvalues of this localized-center portion of the Hamiltonian can be determined by inspection, and are consistent with Hund's rule. The modification leads to nontrivial changes in the properties of the full Anderson Hamiltonian. Within the context of the Hartree-Fock approximation, the likelihood of orbital broken symmetry is reduced.