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We extend the variational cluster approach to deal with
strongly-correlated lattice bosons in the superfluid phase.
To this end, we reformulate the method within a pseudoparticle
formalism, whereby cluster excited states are described in terms
of particle-like excitations.
The approximation amounts to solving a multi-component noninteracting
bosonic system by means of a multi-mode Bogoliubov approximation.
A source-and-drain term is introduced in order to break the
U(1) symmetry at the cluster level. This term must be introduced
whenever the Mott solution becomes unstable.
A criterion for the stability of the solution is discussed.
We provide expressions for the single-particle normal and anomalous Green's functions, the condensate density, the grand-canonical potential, and other static quantities. We apply the method to the two-dimensional Bose-Hubbard model and evaluate results in both Mott and superfluid phase. Our approach yields excellent agreement with Quantum Monte-Carlo calculations. The extension to other problems of interest, such as correlated light-matter systems, Fermi-Bose mixtures, as well as systems out of equilibrium is discussed. |
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