Functional expansion of the Anderson and SU(N) models

Abstract

We study the Anderson and SU(N) lattice models that describe the Kondo and intermediate-valence systems, in the infinite-correlation limit (U\ensuremath{\rightarrow}\ensuremath{\infty}), employing the functional expansion. We use Hubbard operators that describe real electrons. In the lowest, nontrivial approximation, our expressions are similar to, but different from, those derived by several effective-Hamiltonian techniques, like the mean-field slave-boson (MFSB) technique. In the usual large-N limit, our results coincide with those of the equations of motion and Brillouin-Wigner expansions, which are exact in that limit. Our results at T=0 K are compared to those of the MFSB quasiparticle description, and we discuss the two approximations in the region in which they are different. We conclude that although the quasiparticle description should give better results for the thermodynamic properties, our treatment describes in a more physical way the overall behavior of the spectral density of the localized electrons. The structure near the chemical potential that is predicted in other methods is not obtained in our treatment, but I believe that it would appear if a higher-order approximation were employed.