Single-site Anderson model. II Perturbation theory of symmetric model

TL;DR

This paper develops a perturbation theory for the symmetric Anderson model, analyzing impurity electron spectral functions and resonances with strong electron correlations.

Contribution

It formulates an exact Dyson equation and finds approximate correlation functions for the symmetric Anderson model, revealing two symmetric resonances.

Findings

Existence of two symmetric resonances in the spectral function.

Smooth behavior of the spectral function near the Fermi surface.

Resonance widths and heights are quantitatively determined.

Abstract

The strong electron correlations caused by Coulomb interaction of impurity electrons are taken into account. The infinite series of diagrams containing irreducible Green's functions are summed. For symmetric Anderson model we establish the antisymmetry property of the impurity Green's function, formulate the exact Dyson type equation for it, find the approximate correlation function $Z_{\sigma}(i\omega $) and solve the integral equation which determines the full propagator of the impurity electrons. Analytical continuation of the obtained Matsubara Green's function determines the retarded one and gives the possibility to find the spectral function of impurity electrons. The existence of two resonances of this function has been proved. The smooth behaviour was found near the Fermi surface. The two resonances situated symmetrical to the Fermi surface correspond to the energies of quantum transitions of the impurity electrons. The widths and heights of these resonances are established.