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Physics Letters A

Bose–Hubbard phase transition with two- and three-body interaction in a magnetic field

Beibing Huang, Shaolong Wan

Published Aug 26, 2010• 3 citations
Publisher
DOI
10.1016/j.physleta.2010.08.057

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We explore the effects of a repulsive three body interaction and a synthetic gauge field on a spin-1 ultracold Bose gas on an optical lattice to study the quantum phase transition from a supeifluid (SF) to Mon insulating (MI) phase. Both effects being experimentally feasible to achieve, we also add an external Zeeman field to explore an interesting interplay among three of them. A site decoupling mean field technique, known to be an efficient marker of different quantum phases for a spinor Bose Hubbard model, is employed. Without the magnetic fields, the presence of three body interaction stabilizes all the MI lobes, excepting the first one, compared to the SF phase while in presence of the magnetic fields, the spin nematic MI phase makes inroad into the SF phase at the expense of the spin singlet MI phase.
A first-order type phase transition between Mott lobes has been reported in Phys. Rev. Lett. 109, 135302 (2012) for a two-dimensional Bose-Hubbard model in the presence of an attractive three-body interaction. We revisit the scenario in systems of ultracold bosons both in one- and two-dimensional lattices using the density matrix renormalization group method and the self-consistent cluster mean-field theory approach, respectively. We show that an unconventional pairing of particles occurs due to the competing repulsive two-body and attractive three-body interactions. This leads to a pair superfluid phase sandwiched between the Mott insulator lobes corresponding to densities density one and three in the strongly interacting regime. This is in contrast to the direct first-order jump as predicted before. Interestingly, the Mott to pair superfluid phase transitions are found to be continuous in nature. We also show that the pair superfluid phase is robust with respect to the ratio between the two- and three-body interaction strengths. In the end, we establish a connection between the Bose-Hubbard model presented in Phys. Rev. Lett. 109, 135302 (2012) with a more general Bose-Hubbard model and analyze the fate of the pair superfluid phase in the presence of an external trapping potential.
An effective action for Bose-Hubbard model with two- and three-body on-site interaction in a square optical lattice is derived in the frame of a strong-coupling approach developed by Sengupta and Dupuis. From this effective action, superfluid-Mott insulator (MI) phase transition, excitation spectrum and momentum distribution for two phases are calculated by taking into account Gaussian fluctuation about the saddle-point approximation. In addition the effects of three-body interaction are also discussed.