Effects of an attractive three-body interaction on a spin-1 Bose Hubbard model

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.