Variational cluster approach to correlated electron systems in low dimensions

A self-energy-functional approach is applied to construct cluster approximations for correlated lattice models. It turns out that the cluster-perturbation theory [D. Senechal et al., Phys. Rev. Lett. 84, 522 (2000)] and the cellular dynamical mean-field theory [G. Kotliar et al., Phys. Rev. Lett. 87, 186401 (2001)] are limiting cases of a more general cluster method. The results for the one-dimensional Hubbard model are discussed with regard to boundary conditions, bath degrees of freedom, and cluster size.