Abstract We study the effects of an attractive three-body interaction potential on a spin-1 ultracold Bose gas using the mean field approach (MFA). For an antiferromagnetic interaction, the third Mott insulator (MI) lobe is predominantly affected, where it completely engulfs the second and the fourth MI lobes at large values of interaction strength. However, no significant change is observed beyond the fourth MI lobe. The formation of the spin singlet (nematic) MI phase and the different order of phase transitions to the superfluid phase have been carefully scrutinized with the help of spin eigenvalues and the spin nematic order parameter. In the ferromagnetic case, the phase diagram shows similar features to that of a scalar Bose gas. We have compared our results on the MFA phase diagrams for both types of interaction potential via a perturbation expansion in both cases.
We present a semiclassical perspective of the topological Bose-Hubbard model recently studied by quantum Monte Carlo (QMC) simulation on the honeycomb lattice [Phys. Rev. B 93, 121401(R) (2016)]. The three insulating phases uncovered by QMC are as follows: a superfluid, a Mott phase, and a charge-density-wave insulating phase. We show that this model maps to a spin-
1/2 quantum XY model with competing magnetic fields on the two honeycomb sublattices. We give an explicit analytical origin of the quantum phase diagram using mean-field theory. Basically, the competition between the sublattice magnetic fields leads to three distinct phases uncovered by QMC. We find that the mean-field phase diagram captures a large regime of the quantum phase diagram. Furthermore, due to the mapping from bosons to spin variables and vice versa, the bosonic excitations of the Bose-Hubbard model correspond to the magnon excitations of the quantum spin system. We corroborate this assertion by computing the magnon bulk bands and the Berry curvatures and we find that the Berry curvatures have the same trends as the QMC result.