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Journal of Physics Conference Series

Effect of dominant three-body interaction in two-dimensional square lattice

Ying Liang, Huaiming Guo

Published Dec 17, 2012• 3 citations
Publisher

Abstract

The effect of dominant three-body interaction to hard-core boson Hubbard model is studied on a two-dimensional square lattice. In terms of quantum Monte Carlo method, it is shown explicitly a ρ = 2/3 solid phase with coexistence of charge-density-wave and bond orders appears due to the presence of the dominant three-body interaction. For strong three-body interaction, the ρ = 2/3 solid phase appears between superfluid phases and shrinks as decreasing the strength of the three-body interaction, forming a lobe structure in the phase diagram. For weak three-body interactions, superfluid phase exists for the whole range of hard-core densities except the full filled case, where the system is a Mott insulator.

DOI
10.1088/1742-6596/400/1/012040

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The effect of dominant three-body interaction to hard-core boson Hubbard model is studied on a two-dimensional square lattice. In terms of quantum Monte Carlo method, it is shown explicitly a ρ = 2/3 solid phase with coexistence of charge-density-wave and bond orders appears due to the presence of the dominant three-body interaction. For strong three-body interaction, the ρ = 2/3 solid phase appears between superfluid phases and shrinks as decreasing the strength of the three-body interaction, forming a lobe structure in the phase diagram. For weak three-body interactions, superfluid phase exists for the whole range of hard-core densities except the full filled case, where the system is a Mott insulator.
The effect of dominant three-body interaction to the hard-core boson Hubbard model is studied on a two-dimensional square lattice. In terms of the quantum Monte Carlo method, a ? = 2/3 solid phase is shown explicitly with the coexistence of a charge-density wave and a bond-order wave appearing due to the presence of the dominant three-body interaction. For the strong three-body interaction, the ? = 2/3 solid phase appears between superfluid phases and shrinks as the strength of the three-body interaction decreases, forming a lobe structure in the phase diagram. For weak three-body interactions, the superfluid phase exists for the whole range of hard-core densities except the full filled case, where the system is a Mott insulator. Our results may be realized in cold-atom experiments.
We determine the phase diagram of a one-dimensional system of hard-core lattice bosons interacting via repulsive three-body interactions by analytic methods and extensive quantum Monte Carlo simulations. Such three-body interactions can be derived from a microscopic theory for polar molecules trapped in an optical lattice. Depending on the strength of the interactions and the particle density, we find superfluid and solid phases, the latter appearing at an unconventional filling of the lattice and displaying a coexistence of charge-density wave and bond orders.
The two-dimensional square lattice hard-core boson Hubbard model with near-neighbor interactions has a ``checkerboard'' charge density wave insulating phase at half filling and sufficiently large intersite repulsion. When doped, rather than forming a supersolid phase in which long-range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near-neighbor repulsion might similarly stabilize the square lattice supersolid. By considering the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{y}$ directions, we conclude that phase separation still occurs.
The cold atom on a two-dimensional square optical lattice is studied within the hard-core boson Hubbard model with an alternating potential. In terms of the quantum Monte Carlo method, it is shown explicitly that a supersolid phase emerges due to the presence of the alternating potential. For the weak alternating potential, the supersolid state appears for the whole range of hard-core boson densities except the half-filling case, where the system is a Mott insulator. However, for the strong alternating potential, besides the supersolid and Mott insulating states, a charge-density wave phase appears.
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.
By using an unbiased quantum Monte Carlo method, we investigate the hard-core Bose-Hubbard model on a square lattice with the anisotropic dipole-dipole interaction. To study the effect of the anisotropy, dipole moments are assumed to be polarized in the yyy direction on the two-dimensional xyxyxy plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an O(N)O(N)O(N) Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid phase and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multiple plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.