A srtong coupling diagrammatic approach to the single-site Anderson model

A diagrammatic theory around the atomic limit is proposed for the single-impurity Anderson model in which the strongly correlated impurity electrons hybridize with free (uncorrelated) conduction electrons.We have formulated the Generalized Wick's Theorem (GWT)for local electrons preserving the ordinary Wick's theorem for conduction electrons.Our GWT allows us to determine theirreducible Green's functions as the Kubo cumulants. Using this diagrammatic approach, we prove theexistence of a linked cluster theorem for the vacuum diagrams and derive Dyson type of equations for the localized and conduction electron Green's functions and corresponding equations for the mixed propagators. The special approximation for the correlationfunction ,which contains charge and spin fluctuations has been proposed giving us the possibility to close the system of equations and to find the solution for the full impuritypropagator.This Matsubara Green's function has been continued analytically to obtain the spectral function of impurity electrons.Two resonances corresponding to the renormalized energies of quantum transitions of single-site impurity have been found.We have shown that some spectral weight is transformed from these two resonances to the energy equal to zero,which corresponds to Fermi surface.The peculiarity at E=0 is the novel result of ouranalysis and although our approximation does not yield yet a Kondo resonance at energy zero it could be relevant to understand some physical properties of our system . All our investigations were realized in the case of symmetric Anderson Model when the Fermi level is situated exactly at the middle distance between two local impurity levels