Disordered spin dependent interactions in a spinor (S=1) Bose gas: A percolation analysis

Spin-1 Bose–Hubbard model with two- and three-body interactions

“…We used the DMRG algorithm to find the phase diagram of a chain of spinor bosons under two-and threebody interactions by calculating the chemical potential to add or remove one particle at the thermodynamic limit for different values of the hopping, when the parameters U 2 , V 0 << U 0 , and V 2 = 2 U2 U0 V 0 are fixed. Mean-field phase diagrams for this problem were recently reported by Nabi and Basu [44], and we show them in Fig. 4a and Fig.…”

“…This figure shows us that a quantum phase transition from a superfluid state to a Mott insulator one will take place as the hopping parameter decreases as the two-and three-body interactions between spinor bosons are considered. The above conclusion is expected when we are studying interacting bosons; however, the most interesting problem is related to the phase diagram, for which recent mean-field studies suggest that the even-odd asymmetry always happens [44].…”

“…To summarize, in the present paper, we used the density matrix renormalization group to study the ground state of spin-1 bosons loaded into a onedimensional optical lattice interacting via two-and three-body spin dependent and independent interaction terms, considering only antiferromagnetic interaction. The ground state can be Mott insulator or superfluid, and the border between them was found for different sets of the interaction parameters, showing that the well-known even-odd asymmetry for the case with only two-body interactions does not obtain and depends on the relative values of the two-and three-body interactions, contradicting the mean-field results of Nabi and Basu, who suggested that the even-odd asymmetry persists [44]. We found that the three-body interactions do not alter the kind of transition, i.e.…”

“…1 for a finite chain with L = 28 sites, a fixed hopping t/U 0 = 0.10, and interaction parameters U 2 /U 0 = 0.05, V 0 /U 0 = 0.10, and V 2 /U 0 = 0.01. The above parameters were chosen taking into account a recent mean-field calculation about spinor bosons with two-and three-body interactions [44]. We observe that the chemical potential increases monotonously as the global density grows, but at integer densities a plateau appears, which indicates that a finite energy gap was found for integer densities and the ground state corresponds to an incompressible Mott insulator at the thermodynamic limit.…”

“…The phase diagram of spin-1 bosons under twoand three-body interactions was calculated by Nabi and Basu using mean-field theory [44]. They found that as the area of the Mott lobes increases with respect to the superfluid region, the critical point of the superfluid-Mott insulator transition moves to larger values of the hopping with the strength of the three-body interaction term, and they concluded that for antiferromagnetic interactions, the even-odd asymmetry remains.…”