Variational cluster approach to the single-impurity Anderson model

We study the single-impurity Anderson model by means of cluster perturbation theory and the variational cluster approach (VCA). An expression for the VCA grand potential for a system in a noninteracting bath is presented. Results for the single-particle dynamics in different parameter regimes are shown to be in good agreement with established renormalization group results. We aim at a broad and comprehensive overview of the capabilities and shortcomings of the methods. We address the question as to what extent the elusive low-energy properties of the model are reproducible within the framework of VCA. These are furthermore benchmarked against continuous-time quantum Monte Carlo calculations. We also discuss results obtained by an alternative, i.e., self-consistent formulation of VCA, which was introduced recently in the context of nonequilibrium systems.