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We study the single impurity Anderson model by means of cluster perturbationtheory and the variational cluster approach (VCA). An expression for the VCAgrand potential for a system in a non interacting bath is presented. Resultsfor the single-particle dynamics in different parameter regimes are shown to bein good agreement with established renormalization group results. We aim at abroad and comprehensive overview of the capabilities and shortcomings of themethods. We address the question to what extent the elusive low energyproperties of the model are reproducible within the framework of VCA. These arefurthermore benchmarked against continuous time quantum Monte Carlocalculations. We also discuss results obtained by an alternative, i.e. selfconsistent formulation of VCA, which was introduced recently in the context ofnon equilibrium systems.

Variational cluster approach to the single impurity Anderson model