Variational cluster perturbation theory for Bose–Hubbard models

We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator-to-superfluid transition in the Bose–Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum—free of spurious gaps—despite the fact that it formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimensional dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed.