Bosonic Fractional Quantum Hall States in Rotating Optical Lattices: Projective Symmetry Group Analysis

We study incompressible ground states of bosons in a two-dimensional rotating square optical lattice. The system can be described by the Bose-Hubbard model in an effective uniform magnetic field present due to the lattice rotation. To study ground states of the system, we map it to a frustrated spin model, followed by Schwinger boson mean field theory and projective symmetry group analysis. Using symmetry analysis we identify bosonic fractional quantum Hall states, predicted for bosonic atoms in rotating optical lattices, with possible stable gapped spin liquid states within the Schwinger boson formalism. In particular, we find that previously found fractional quantum Hall states induced by the lattice potential, and with no counterpart in the continuum [G. M\"oller, and N. R. Cooper, Phys. Rev. Lett. \textbf{103}, 105303 (2009)], correspond to "$\pi$ flux" spin liquid states of the frustrated spin model.