Analytical approximation for single-impurity Anderson model
We have applied the recently developed dual fermion technique to the spectral properties of single-band Anderson impurity problem (SIAM). In our approach a series expansion is constructed in vertices of the corresponding atomic Hamiltonian problem. This expansion contains a small parameter in two limiting cases: in the weak coupling case ($U/t \to 0$), due to the smallness of the irreducible vertices, and near the atomic limit ($U/t \to \infty$), when bare propagators are small. Reasonable results are obtained also for the most interesting case of strong correlations ($U \approx t$). The atomic problem of the Anderson impurity model 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 renormalized atomic problem. Formulae for the first-order dual diagram correction are obtained analytically in the real-time domain. Most of the Kondo-physics is reproduced: logarithmic contributions to the self energy arise, Kondo-like peak at the Fermi level appears, and the Friedel sum rule is fulfilled. Our approach describes also renormalization of atomic resonances due to hybridization with a conduction band. A generalization of the proposed scheme to a multi-orbital case can be important for the realistic description of correlated solids.