We study a model of strongly interacting lattice bosons with a Gutzwiller-type wave function that contains only on-site correlations. The variational energy and the condensate fraction associated with the variational wave function are exactly evaluated for both finite and infinite systems and compared with exact quantum Monte Carlo results in two dimensions. This ansatz for the wave function gives the correct qualitative picture of the phase diagram of this system; at commensurate densities, this system enters a Mott-insulator phase for large values of the interaction.
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Krauth et al. (1992) studied this question.