  We introduce a new numerical method for the solution of self-consistent
equations in the cluster mean-field theory. The method uses the density matrix
renormalization group method to solve the associated cluster problem. We obtain
an accurate critical value of the supersolid-superfluid transitions in the
hard-core bosonic Hubbard model on a triangular lattice, which is comparable
with the recent quantum Monte Carlo results. This algorithm is applicable to
more general classes of models with a larger number of degrees of freedom.
