Abstract
We study the effects of a three-body interaction potential on a spin-1 ultracold Bose gas using mean-field approach (MFA). For an antiferromagnetic (AF) interaction, we have found the existence of the odd-even asymmetry in the Mott insulating (MI) lobes in the presence of both the repulsive two- and three-body interactions. In case of a purely three-body repulsive interaction, the higher-order MI lobes stabilize against the superfluid phase. Also the spin nematic (singlet) formation occurs for all the odd (even) MI lobes for the former, while there is neither any asymmetry, nor spin nematic (singlet) formation being observed for the latter case. The results are confirmed after carefully scrutinizing the spin eigenvalue and spin nematic order parameter for both the cases. We have compared our MFA results with the analytic phase diagrams obtained using a perturbation mean-field (PMFA) expansion.
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