Variational cluster approach to the single impurity Anderson model

TL;DR

This paper applies the variational cluster approach to the single impurity Anderson model, demonstrating its effectiveness in capturing low-energy properties and benchmarking against quantum Monte Carlo results.

Contribution

It introduces a grand potential expression for VCA in non-interacting baths and compares VCA's capabilities with established methods for the Anderson model.

Findings

VCA results agree well with renormalization group data

The method reproduces low-energy properties effectively

Benchmarking shows VCA's strengths and limitations

Abstract

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 non interacting 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 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 non equilibrium systems.