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Physics Letters A

Temperature effects on superfluid phase transition in Bose–Hubbard model with three-body interaction

T. K. Kopeć, Michał Szymański

Published Oct 1, 2014• 5 citations
Publisher
DOI
10.1016/j.physleta.2014.10.002

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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.
We study the two-dimensional Bose-Hubbard model in the presence of a three-body interaction term, both at a mean-field level and via quantum Monte Carlo simulations. The three-body term is tuned by coupling the triply occupied states to a trapped universal trimer. We find that, for a sufficiently attractive three-body interaction, the n=2 Mott lobe disappears and the system displays first-order phase transitions separating the n=1 from the n=3 lobes and the n=1 and n=3 Mott insulator from the superfluid. We also analyze the effect of finite temperature and find that transitions are still of first order at temperatures T~J, where J is the hopping matrix element.