Renormalized perturbation calculations for the single-impurity Anderson model

We illustrate the renormalized perturbation expansion method by applying it to a single-impurity Anderson model. Previously, we have shown that this approach gives the exact leading-order results for the specific heat, spin and charge susceptibilities and leading-order temperature dependence of the resistivity for this model in the Fermi-liquid regime, when carried out to second order in the renormalized interaction (U) over tilde. Here we consider the effects of higher-order quasiparticle scattering and calculate the third-order contributions to the H-3-term in the impurity magnetization for the symmetric model in a weak magnetic field H. The result is asymptotically exact in the weak-coupling regime, and is very close to the exact Bethe ansatz result in the Kondo regime. We also calculate the quasiparticle density of states in a magnetic field, which is of interest in relation to recent experimental work on quantum dots.