  We present the novel approach to the Bose-Hubbard model using the
$\mathrm{U}(1)$ quantum rotor description. The effective action formalism
allows us to formulate a problem in the phase only action and obtain an
analytical formulas for the critical lines. We show that the nontrivial
$\mathrm{U}(1)$ phase field configurations have an impact on the phase
diagrams. The topological character of the quantum field is governed by terms
of the integer charges - winding numbers. The comparison presented results to
recently obtained quantum Monte Carlo numerical calculations suggests that the
competition between quantum effects in strongly interacting boson systems is
correctly captured by our model.

Statistical Mechanics