Composite Fermion Theory for Bosonic Quantum Hall States on Lattices

We study the groundstates of the Bose-Hubbard model in a uniform effective magnetic field, illustrating the physics of cold atomic gases on `rotating optical lattices'. Mapping the bosons to composite fermions leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial wavefunctions for these phases, and perform numerical tests of the predictions of the composite fermion model. Our results establish the existence of strongly correlated phases beyond those in the continuum limit, and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau-level.