Renormalized parameters and perturbation theory for an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-channel Anderson model with Hund’s rule coupling: Symmetric case

Abstract

We extend the renormalized perturbation theory for the single-impurity Anderson model to the $n$-channel model with a Hund's rule coupling, and show that the exact results for the spin, orbital, and charge susceptibilities, as well as the leading low-temperature dependence for the resistivity, are obtained by working to second order in the renormalized couplings. A universal relation is obtained between the renormalized parameters, independent of $n$, in the Kondo regime. An expression for the dynamic spin susceptibility is also derived by taking into account repeated quasiparticle scattering, which is asymptotically exact in the low-frequency regime and satisfies the Korringa-Shiba relation. The renormalized parameters, including the renormalized Hund's rule coupling, are deduced from numerical renormalization-group calculations for the model for the case $n=2$. The results confirm explicitly the universal relations between the parameters in the Kondo regime. Using these results, we evaluate the spin, orbital, and charge susceptibilities, temperature dependence of the low-temperature resistivity, and dynamic spin susceptibility for the particle-hole symmetric regime of the $n=2$ model.