We investigate the phase diagram of a two-species Bose-Hubbard model
describing atoms and molecules on a lattice, interacting via a Feshbach
resonance. We identify a region where the system exhibits an exotic super-Mott
phase and regions with phases characterized by atomic and/or molecular
condensates. Our approach is based on a recently developed exact quantum Monte
Carlo algorithm: the Stochastic Green Function algorithm with tunable
directionality. We confirm some of the results predicted by mean-field studies,
but we also find disagreement with these studies. In particular, we find a
phase with an atomic but no molecular condensate, which is missing in all
mean-field phase diagrams.Comment: 4 pages, 6 figure