  We investigate the zero-temperature phase diagram of interacting Bose gases
in the presence of a simple cubic optical lattice, going beyond the regime
where the mapping to the single-band Bose-Hubbard model is reliable. Our
computational approach is a new hybrid quantum Monte Carlo method which
combines algorithms used to simulate homogeneous quantum fluids in continuous
space with those used for discrete lattice models of strongly correlated
systems. We determine the critical interaction strength and optical lattice
intensity where the superfluid-to-insulator transition takes place, considering
also the regime of shallow optical lattices and strong inter-atomic
interactions. The implications of our findings for the super-solid state of
matter are discussed.
