In this Brief Report the extended Bose-Hubbard model with local two- and three-body interactions is studied by the exact diagonalization approach. The shapes of the first two insulating lobes are discussed and the values of the critical tunneling for which the insulating phase loses stability for repulsive and attractive three-body interactions are predicted.

arXiv:1202.1932Physical Review AJun 26, 201245 citations

arXiv:1707.08195 · Physics Letters A

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

A. F. Hincapie-F, R. Franco, Jereson Silva-Valencia

Published Apr 20, 2018• 3 citations

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DOI: 10.1016/j.physleta.2018.04.029

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Using the density-matrix renormalization-group method, we studied the ground state of the one-dimensional

S=1

Bose-Hubbard model with local three-body interactions, which can be a superfluid or a Mott insulator state. We drew the phase diagram of this model for both ferromagnetic and antiferromagnetic interaction. Regardless of the sign of the spin-dependent coupling, we obtained that the Mott lobes area decreases as the spin-dependent strength increases, which means that the even-odd asymmetry of the two-body antiferromagnetic chain is absent for local three-body interactions. For antiferromagnetic coupling, we found that the density drives first-order superfluid-Mott insulator transitions for even and odd lobes. Ferromagnetic Mott insulator and superfluid states were obtained with a ferromagnetic coupling, and a tendency to a ``long-range'' order was observed.