Quantum phases of a spin-1 ultracold Bose gas with three-body interactions

Abstract

We study the effects of both a repulsive and an attractive 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 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. However, the spin nematic (singlet) formation is restricted upto the first (second) MI lobes for the former one, while there is neither any asymmetry nor spin nematic (singlet) formation is observed for the later case. The results are confirmed after carefully scrutinizing the spin eigen value and spin nematic order parameter for both the cases. On the other hand, for an attractive three body interaction, the third MI lobe is predominantly affected, where it completely engulfs the second and the fourth MI lobes at large values of the interaction strength. Albeit no significant change is observed beyond the fourth MI lobe. In the ferromagnetic case, the phase diagram shows similar features as that of a scalar Bose gas. We have compared our results on the MFA phase diagrams for both types of the interaction potential via a perturbation expansion in both the cases.

Interplay of the Staggered and Three‐Body Interaction Potentials on the Quantum Phases of a Spin‐1 Ultracold Atom in an Optical Lattice

“…Further rise to $$\lambda =1.0\nobreakspace \text{W}$$ makes $$\rho _{i}\le 2$$ insulating lobes to disappear but helps in stabilizing the higher densities with $$\rho _{i}\ge 3$$ and thereby affects the odd–even asymmetry in the MI phase. Moreover, the spin eigenvalue and nematic order parameter variation in the MI and DW phases tells that $$\langle {{\bf S}}_{\alpha }^{2} \rangle =2$$ and $$Q^{\alpha }_{zz}\ne 0$$ for $$\rho _{i}=3$$ and $$\langle {{\bf S}}_{\alpha }^{2} \rangle =Q^{\alpha }_{zz}= 0$$ for $$\rho _{i}=4$$ but follow an oscillatory behavior for $$\rho _{i}=2$$ occupation lobes for both values of $$\lambda /W$$ [ 97 ] (Figure 6b). This outlines that spin singlet formation is possible for other even occupation densities except $$\rho _{i}=2$$ lobe.…”

“…Further rise to 𝜆 = 1.0 W makes 𝜌 i ≤ 2 insulating lobes to disappear but helps in stabilizing the higher densities with 𝜌 i ≥ 3 and thereby affects the odd-even asymmetry in the MI phase. Moreover, the spin eigenvalue and nematic order parameter variation in the MI and DW phases tells that ⟨S 2 𝛼 ⟩ = 2 and Q 𝛼 zz ≠ 0 for 𝜌 i = 3 and ⟨S 2 𝛼 ⟩ = Q 𝛼 zz = 0 for 𝜌 i = 4 but follow an oscillatory behavior for 𝜌 i = 2 occupation lobes for both values of 𝜆∕W [97] (Figure 6b). This outlines that spin singlet formation is possible for other even occupation densities except 𝜌 i = 2 lobe.…”

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

“…The phase diagrams in Fig. 2(a) and (b) show that, unlike the repulsive three body interaction [38], which retains the odd-even asymmetry in the MI lobes, here the attractive three body interaction diminishes the odd-even asymmetry around the second and the fourth MI lobes. This typically raises one concern, namely, whether will there any such asymmetry sustain beyond the fourth MI lobe.…”

“…Apart from studying such properties in presence of two body interactions cited above, recently, the consequences of higher body interaction, such as a repulsive three body interaction on the ground state phase diagrams have been explored on a spin-1 ultracold Bose gas using MFA in chapter 6 and DMRG [36,37] techniques. Interestingly, the mean field phase diagram still shows a spin nematic-singlet formation and hence an asymmetry in the MI phase in presence of both the two and three body interactions, while for a purely three body interaction such asymmetry is destroyed [38]. On the contrary, the DMRG studies show that there is neither any asymmetry, nor any spin singlet-nematic formation in the MI phase and there is a possible phase transition involved in the SF phase in presence of both the two and three body interactions [36,37].…”

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

“…Apart from studying such properties in the presence of the two-body interactions cited above, recently, the consequences of a higher body interaction, such as a repulsive three-body interaction, on the ground state phase diagrams have been explored on a spin-1 ultracold Bose gas using MFA [38] and DMRG [36,37] techniques. Interestingly, the mean field phase diagram still shows a spin nematic-singlet formation and hence an asymmetry in the MI phase in the presence of both the two-and threebody interactions, while for a purely three-body interaction such asymmetry is destroyed [38]. On the contrary, the DMRG studies show that there is neither any asymmetry, nor any spin singlet-nematic formation in the MI phase and there is a possible phase transition involved in the SF phase in the presence of both the two-and three-body interactions [36,37].…”