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The interplay between magnetism and metal-insulator transitions isfundamental to the rich physics of the single band fermion Hubbard model (FHM).Recent progress in experiments on trapped ultra-cold atoms have made possiblethe exploration of similar effects in the boson Hubbard model (BHM). This paperreports Quantum Monte Carlo (QMC) simulations of the spin-1 BHM in the groundstate. In the case of antiferromagnetic interactions, which favor singletformation within the Mott insulator lobes, we present exact numerical evidencethat the superfluid-insulator phase transition is first (second) orderdepending 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 ofattractive spin interactions and demonstrate the existence of the ferromagneticsuperfluid. We also compare the QMC phase diagram with a third orderperturbation calculation.

Magnetic and Superfluid Transitions in the d=1 Spin-1 Boson Hubbard Model