  We discuss the ground state of the two-dimensional Bose-Hubbard (BH)
Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by
employing \mathrm{U}\left(1\right) quantum rotor approach and the topologically
constrained path integral that includes a summation over
\mathrm{U}\left(1\right) topological charge. We derive an effective quantum
action for the BH model, which enables a non-perturbative treatment of the
zero-temperature phase transition. We calculate the ground-state phase diagram,
analytically deriving maximum repulsive energy for several rational values of
the frustration rotation parameter f=0, 1/2, 1/3, 1/4, and 1/6 for the square
and triangular lattice, which improves upon previous theoretical treatments.
The ground state of the rotating Bose-Einstein condensates on a triangular
lattice appears to be most stable against the effects of rotation. Performed
calculations revealed strong dependence of the critical ratio of the kinetic
energy to the repulsive on-site energy, that separates the global coherent from
the insulating state, on topology of the lattice.
