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Bulletin of the American Physical Society

First order SF-MI transition in the Bose-Hubbard model with tunable three-body onsite interaction

Barbara Capogrosso-Sansone, Arghavan Safavi-Naini, Javier von Stecher, Seth T. Rittenhouse

Published Jun 7, 2012• 0 citations
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Abstract

Homer L. Dodge Department of Physics and Astronomy,The University of Oklahoma, Norman, Oklahoma ,73019, USA(Dated: February 20, 2012)We study the two-dimensional Bose-Hubbard model in the presence of a 3-body interaction term,both at a mean eld level and via quantum Monte Carlo simulations. The 3-body term is tunedby coupling the triply occupied states to a trapped universal trimer. We nd that, for sucientlyattractive 3-body interaction the n= 2 Mott lobe disappears and the system displays rst orderphase transitions separating the n= 1 from the n= 3 lobes, and the n= 1 and n= 3 Mottinsulator from the superuid. We have also analyzed the e ect of nite temperature and found thattransitions are still of rst order at temperatures T˘J.

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Homer L. Dodge Department of Physics and Astronomy,The University of Oklahoma, Norman, Oklahoma ,73019, USA(Dated: February 20, 2012)We study the two-dimensional Bose-Hubbard model in the presence of a 3-body interaction term,both at a mean eld level and via quantum Monte Carlo simulations. The 3-body term is tunedby coupling the triply occupied states to a trapped universal trimer. We nd that, for sucientlyattractive 3-body interaction the n= 2 Mott lobe disappears and the system displays rst orderphase transitions separating the n= 1 from the n= 3 lobes, and the n= 1 and n= 3 Mottinsulator from the superuid. We have also analyzed the e ect of nite temperature and found thattransitions are still of rst order at temperatures T˘J.
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.
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.
We study the Extended Bose-Hubbard Model with a three-body onsite interaction. Using an exact diagonalization method and a variational Matrix Product States algorithm, \emph{Alps mps-optim}, we compute and analyse the energy charge gap and finite system correlation functions to obtain the phase boundaries and determine the phases and phase transitions of the model. For \mbox{VU=0.6\frac{V}{U} = 0.6UV​=0.6} and \mbox{WU=0\frac{W}{U} = 0UW​=0}, we observed the emergence of the Haldane insulator (HI) phase at the tip of the \mbox{ρ=1ρ= 1ρ=1} charge density wave (CDW) lobe and for \mbox{VU=0.6\frac{V}{U} = 0.6UV​=0.6} and \mbox{WU=1\frac{W}{U} = 1UW​=1}, we observed the emergence of the supersolid (SS) phase at the tip of the \mbox{ρ=1/2ρ= 1/2ρ=1/2} charge density wave (CDW) lobe. We also noticed that the effect of the inclusion of both the three-body onsite and nearest neighbor interactions on the phase diagram of the model for filling factor \mbox{ρ=2ρ= 2ρ=2} is to stabilize the Mott insulator (MI) phase such that the system remains in the MI phase for all values of VU\frac{V}{U}UV​.
The Bose-Hubbard model describes the physics of a system of bosonic ultracold atoms in an optical lattice, in which a phase transition is present between a superfluid phase and a Mott insulator one. \nThe exact solution of this Hamiltonian is only feasible to find the ground-state of small systems, while other techniques (as mean-field schemes or quantum Monte Carlo) are necessary to study systems of larger size. \n \nAs a first application, we study the trapped model - relevant for the comparison with current experiments - through an inhomogeneous mean-field scheme. We describe some signatures of the phase crossover between superfluid and Mott insulator. In particular, the visibility of the quasimomentum distribution shows some kinks as a function of the lattice depth; we describe these features and we link them with the ones observed in other works in the literature. \n \nAs a second application, we use quantum Monte Carlo techniques to study the one-dimensional Bose-Hubbard model with long-range interactions and we focus on the appearance of the Haldane insulating phase, distinguishable from the Mott one through the presence of non-local hidden order. \nNon-local correlation functions are also used to describe the difference between the superfluid phase and the Mott insulator one.
The Bose–Hubbard model with an effective off-site three-body tunneling, characterized by jumps towards one another, between one atom on a site and a pair atoms on the neighborhood site, is studied systematically on a one-dimensional (1D) lattice, by using the density matrix renormalization group method. The off-site trimer superfluid, condensing at momentum k = 0 , emerges in the softcore Bose–Hubbard model but it disappears in the hardcore Bose–Hubbard model. Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from [ Phys. Rev. A 81 , 011601(R) (2010)] is stable in the thermodynamic limit. The off-site trimer superfluid phase, the partially off-site trimer superfluid phase and the Mott insulator phase are found, as well as interesting phase transitions, such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase. Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.