Variational exact diagonalization method for Anderson impurity models

We describe a variational approach to solving Anderson impurity models by means of exact diagonalization. Optimized parameters of a discretized auxiliary model are obtained on the basis of the Peierls-Feynman-Bogoliubov principle. Thereby, the variational approach resolves ambiguities related to the bath discretization, which is generally necessary to make Anderson impurity models tractable by exact diagonalization. The choice of variational degrees of freedom made here allows systematic improvements of total energies over mean-field decouplings like Hartree-Fock. Furthermore, our approach allows us to embed arbitrary bath discretization schemes in total-energy calculations and to systematically optimize and improve on traditional routes to the discretization problem such as fitting of hybridization functions on Matsubara frequencies. Benchmarks in terms of a single orbital Anderson model demonstrate that the variational exact diagonalization method accurately reproduces free energies as well as several single- and two-particle observables obtained from an exact solution. Finally, we demonstrate the applicability of the variational exact diagonalization approach to realistic five-orbital problems with the example system of Co impurities in bulk Cu and compare it to continuous-time Monte Carlo calculations. The accuracy of established bath discretization schemes is assessed in the framework of the variational approach introduced here.