Alternative self-energy expression for the Anderson model

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Abstract
A closed system of equations for the Green’s functions is found by applying the functional-derivative technique at the third level in the coupled chain of equations. From this set of equations an exact expression for the impurity atom’s self-energy is obtained which involves only first-order functional derivatives. A procedure is proposed for generating nonperturbative solutions to arbitrary accuracy in a systematic manner. As an illustration, a solution is presented in which the functional derivatives are evaluated using the Hartree-Fock approximation. The spectral density function is calculated for the symmetric case and is found to have the correct behavior for all values of U/Δ.