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We extend the variational cluster approach to deal with strongly correlatedlattice bosons in the superfluid phase. To this end, we reformulate theapproach within a pseudoparticle formalism, whereby cluster excitations aredescribed by particlelike excitations. The approximation amounts to solving amulticomponent noninteracting bosonic system by means of a multimode Bogoliubovapproximation. A source-and-drain term is introduced in order to break U(1)symmetry at the cluster level. We provide an expression for the grandpotential, the single-particle normal and anomalous Green's functions, thecondensate density, and other static quantities. As a first nontrivialapplication of the method we choose the two-dimensional Bose-Hubbard model andevaluate results in both the Mott and the superfluid phases. Our results showan excellent agreement with quantum Monte Carlo calculations.

Variational cluster approach for strongly correlated lattice bosons in the superfluid phase