$$1/(N - 1)$$ Expansion for an SU(N) Impurity Anderson Model: A New Large-N Scheme Based on a Perturbation Theory in U

Abstract

Low-energy properties of an SU(N) Anderson model are studied, using the 1/(N−1)1/(N - 1) expansion based on a perturbation theory in the Coulomb interaction U. This approach is different from conventional large N theories, such as from the usual 1 ∕ N expansion and the non-crossing approximation based on the expansion in the hybridization matrix element between the impurity orbital and conduction band. In our approach the scaling factor N − 1 appears as the total number of interacting orbitals excluding the one prohibited by the Pauli principle, and it captures the low-energy local Fermi-liquid behavior correctly. We find that the next-leading-order results of the renormalized parameters agree closely with the numerical renormalization group results in a wide range of electron fillings at N = 4, where the degeneracy is still not so large. This ensures the reliability of the next-leading order results for N > 4. Furthermore, we apply this approach to nonequilibrium current through a quantum dot in the Kondo regime.