Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as ${}^{87}\mathrm{Rb},{}^{39}\mathrm{K}$, or ${}^{23}\mathrm{Na}$ in the $F=1$ hyperfine state offer an ideal platform for studying the interplay of superfluidity and quantum magnetism. Motivated by the experimental developments, we study ground-state phases of a two-component Bose gas loaded on an optical lattice. The system is described effectively by the Bose-Hubbard Hamiltonian with on-site and near-neighbor spin-spin interactions. An important feature of our investigation is the inclusion of interconversion (spin-flip) terms between the two species, which has been observed in optical lattice experiments. Using mean-field theory and quantum Monte Carlo simulations, we map out the phase diagram of the system. A rich variety of phases is identified, including antiferromagnetic (AF) Mott insulators and ferromagnetic and AF superfluids.

• Received 4 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.054506