A diagram approach to the strong coupling in the twofold-degenerate Anderson impurity model

Abstract

It is well known that orbital degeneracy plays an essential role in the Mott metal-insulator transition. Here, we study the role of the Hund-rule coupling in an orbitally degenerate model using a diagram approach and taking the intra-atomic Coulomb interactions of two electrons with opposite spins occupying the same or different orbitals into account on an equal footing with the intra-atomic exchange. The investigations are based on our diagram theory for strongly correlated electron systems previously developed for the nondegenerate [1-8] and twofold degenerate [9] models. Our approximation includes only local self-energy terms. It is well known that such an approximation is well justified for a large coordination number. The nonlocal terms [10] corresponding to a higher-order approximation in the inverse coordination number are neglected here. We first determined all the energy eigenfunctions and eigenvalues of the localized d-electron part of the Hamiltonian. We obtained their dependence on the intra- and inter-orbital Coulomb interactions and on the Hund-rule coupling constant. We developed the perturbation theory around the atomic limit and determine the Matsubara Green‘s functions in the normal state. We obtained a Dyson-type equation for these functions and discussed its analytical solutions in detail.