Superfluid-to-Mott insulator transition of bosons with local three-body interactions

Mean-field approaches to the Bose–Hubbard model with three-body local interaction

“…Furthermore, the stability of the Mott lobe increases with increasing of the filling of the lattice. This is also in accordance with recent exact results obtained for the one-dimensional chain in the limit of dominant three-body interactions (U = 0) [13,14] where exactly the same effect was observed. Finally note that at the mean-field level, for general W/U , there is no change in character of MI-SF quantum phase transition which is still of second order.…”

“…A particularly interesting class of such models take into account not only two-but also three-body local interactions. The phase properties of these models have recently been widely discussed in the literature for one dimensional chains using exact diagonalization [10] and Density Matrix Renormalization Group methods [11,12,13,14]. The so-called perturbative single site mean-field approach was used to obtain the qualitative phase boundaries in [15,16] for various parameter regimes.…”

Effective three-body interactions for bosons in a double-well confinement

“…Much progress in these non-standard Hubbard models has been made in recent years, both in theoretical and experimental studies [25]. Among the effects mentioned above, the effective three-body interactions are of particular interest [26][27][28][29][30][31][32][33]. In contrast to the inelastic three-body processes, these effective, coherent three-body interactions are generated by the bosonic two-body interaction-induced virtual excitations to higher bands.…”

Mott lobes of the $S=1$ Bose-Hubbard model with three-body interactions

“…Phase diagrams of spinless bosons under three-body interactions in one dimension have been studied and found by several authors. For instance, bosons under on-site interactions [29][30][31][32], nearest neighbor interaction [33], and contact three body interaction [34] have been considered. An interesting result obtained for the on-site case was that the area of the first Mott lobe (two bosons per site) decreases while the second Mott lobe grows as the threebody strength increases.…”