Abstract
Abstract We revise the simplest possible approximations to solve numerically the vertex equations for the single impurity Anderson model (SIAM) within the finite U non-crossing approximation (UNCA), considering the self-energies at lowest order in the 1 / N diagrammatic expansion. We introduce an approximation to the vertex corrections that includes the double energy dependence and compare it with an approximation (NCAf 2 v) that neglects a second energy argument. Finally, we analyse the influence of the different approximations on the estimated Kondo scale for simple electronic models.
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