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

Frustration effects in rapidly rotating square and triangular optical lattices