  The interplay between magnetism and metal-insulator transitions is
fundamental to the rich physics of the single band fermion Hubbard model (FHM).
Recent progress in experiments on trapped ultra-cold atoms have made possible
the exploration of similar effects in the boson Hubbard model (BHM). This paper
reports Quantum Monte Carlo (QMC) simulations of the spin-1 BHM in the ground
state. In the case of antiferromagnetic interactions, which favor singlet
formation within the Mott insulator lobes, we present exact numerical evidence
that the superfluid-insulator phase transition is first (second) order
depending on whether the Mott lobe is even (odd). In the ferromagnetic case,
the transitions are all continuous. We obtain the phase diagram in the case of
attractive spin interactions and demonstrate the existence of the ferromagnetic
superfluid. We also compare the QMC phase diagram with a third order
perturbation calculation.
