Equation-of-motion treatment of theN-fold-degenerate Anderson model in the large-Nlimit

The periodic Anderson model of magnetic moments within a metal is investigated in the limit of a large spin-orbit degeneracy N of the magnetic ions. It is shown, by means of the equations of motion for the single-particle Green’s function, that an exactly solvable limit U→∞ and N→∞ (U Coulomb correlation) exists under the assumption that the spin-orbit quantum number is also a good quantum number for the conduction band or, equivalently, that there are also N conduction bands. Then it can be shown by means of diagrammatic perturbation theory that a certain decoupling on the third level of the equation-of-motion hierarchy becomes exact in the limit N→∞. Intersite contributions are of order 1/N, so that, except for a chemical-potential renormalization, the lattice is equivalent to $N_s$ independent impurities for N→∞ ($N_s$ number of sites). An integral equation for the one-particle Green’s function, which is exact in these limits, is derived and discussed. This integral equation can be solved analytically for zero temperature. To obtain physically meaningful results one has to include 1/N corrections in which case the equation can only be solved numerically. Results for the spectral function at different temperatures in the Kondo and in the mixed-valence regime are presented. The dependence of the valency on the localized-level position and thus the transition from the Kondo to the mixed-valence regime are investigated. A suitable approximation for the case of finite U is discussed.