Phase boundary of the boson Mott insulator in a rotating optical lattice

We consider the Bose-Hubbard model in a two-dimensional rotating optical lattice and investigate the consequences of the effective magnetic field created by rotation. Using a Gutzwiller-type variational wave function, we find an analytical expression for the Mott insulator (MI)-superfluid (SF) transition boundary in terms of the maximum eigenvalue of the Hofstadter butterfly. The dependence of phase boundary on the effective magnetic field is complex, reflecting the self-similar properties of the single particle energy spectrum. Finally, we argue that fractional quantum Hall phases exist close to the MI-SF transition boundaries, including MI states with particle densities greater than one.