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We introduce a new numerical method for the solution of self-consistentequations in the cluster mean-field theory. The method uses the density matrixrenormalization group method to solve the associated cluster problem. We obtainan accurate critical value of the supersolid-superfluid transitions in thehard-core bosonic Hubbard model on a triangular lattice, which is comparablewith the recent quantum Monte Carlo results. This algorithm is applicable tomore general classes of models with a larger number of degrees of freedom.

Cluster mean-field approach with density matrix renormalization group: Application to the hard-core bosonic Hubbard model on a triangular lattice