Analytical approximation for single-impurity Anderson model

We propose a new renormalized strong-coupling expansion to describe the electron spectral properties of single-band Anderson impurity problem in a wide energy range. The first-order result of our scheme reproduces well the entire single-electron spectrum of correlated impurity with the Kondo-like logarithmic contributions to the self energy and the renormalization of atomic resonances due to hybridization with conduction electrons. The Friedel sum rule for a half-filled system is fulfilled. The approach is based on so-called dual transformation, so that the series is constructed in vertices of the corresponding atomic Hamiltonian problem. The atomic problem of single impurity has a degenerate ground state, so the application of the perturbation theory is not straightforward. We construct a special approach dealing with symmetry-broken ground state of the atomic problem. The renormalization ensures a convergence near the frequencies of atomic resonances. Proposed expansion contains a small parameter in the weak- and in the the strong-coupling case and interpolates well in between. Formulae for the first-order dual diagram correction are obtained analytically in the real-time domain. A generalization of this scheme to a multi-orbital case can be important for the realistic description of correlated solids.