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arXiv:1003.6070 · Physical Review B

Hard core bosons on the dual of the bowtie lattice

Wanzhou Zhang, Laixi Li, Wenan Guo

Published Oct 28, 2010• 5 citations
arXivHTMLPDF

Abstract

We study the zero-temperature phase diagram of hardcore bosons on the dual of the bowtie lattice. Two types of striped diagonal long-range order (striped order I and striped order II) are discussed. A state with type-II striped order and superfluidity is found, even without nearest-neighbor repulsion. The emergence of such a state is due to the inhomogeneity and the anisotropy of the lattice structure. However, neither the translational symmetry nor the symmetry between sublattices of the original lattice is broken in this state. In this paper, we restrict a ``solid state'' of lattice bosons as a diagonal long-range-ordered state breaking either the translational symmetry of the original lattice or the symmetry of different sublattices. We thus name such a phase a striped superfluid phase. In the presence of a nearest-neighbor repulsion, we find two striped charge-density-wave phases with boson density $\ensuremath{\rho}=1/2$ (with striped order I) and $\ensuremath{\rho}=2/3$ (with striped order II), respectively, when the hopping amplitude is small compared with the repulsion. The striped charge-density wave I state is a solid, in which the translational symmetry of the original lattice is broken. We observe a rather special first-order phase transition showing an interesting multiloop hysteresis phenomenon between the two striped charge-density-wave phases when the hopping term is small enough. This can be accounted for by the special degeneracy of the ground states near the classical limit. The striped superfluid phase reappears outside the two striped charge-density-wave phases. The transition between the striped charge-density wave I and striped superfluid phases is first order while the transition between striped charge-density wave II and the striped superfluid phases is continuous. We find that the superfluid stiffness is anisotropic in the striped superfluid states with and without repulsion. In the striped superfluid state with repulsion, the superfluid stiffness is subject to different types of anisotropy in the region near half filling and above 2/3 filling.

DOI
10.1103/physrevb.82.134536

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We study the zero-temperature phase diagram of hardcore bosons on the dual of the bowtie lattice. Two types of striped diagonal long-range order (striped order I and striped order II) are discussed. A state with type-II striped order and superfluidity is found, even without nearest-neighbor repulsion. The emergence of such a state is due to the inhomogeneity and the anisotropy of the lattice structure. However, neither the translational symmetry nor the symmetry between sublattices of the original lattice is broken in this state. In this paper, we restrict a ``solid state'' of lattice bosons as a diagonal long-range-ordered state breaking either the translational symmetry of the original lattice or the symmetry of different sublattices. We thus name such a phase a striped superfluid phase. In the presence of a nearest-neighbor repulsion, we find two striped charge-density-wave phases with boson density \ensuremathρ=1/2\ensuremath{\rho}=1/2\ensuremathρ=1/2 (with striped order I) and \ensuremathρ=2/3\ensuremath{\rho}=2/3\ensuremathρ=2/3 (with striped order II), respectively, when the hopping amplitude is small compared with the repulsion. The striped charge-density wave I state is a solid, in which the translational symmetry of the original lattice is broken. We observe a rather special first-order phase transition showing an interesting multiloop hysteresis phenomenon between the two striped charge-density-wave phases when the hopping term is small enough. This can be accounted for by the special degeneracy of the ground states near the classical limit. The striped superfluid phase reappears outside the two striped charge-density-wave phases. The transition between the striped charge-density wave I and striped superfluid phases is first order while the transition between striped charge-density wave II and the striped superfluid phases is continuous. We find that the superfluid stiffness is anisotropic in the striped superfluid states with and without repulsion. In the striped superfluid state with repulsion, the superfluid stiffness is subject to different types of anisotropy in the region near half filling and above 2/3 filling.
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We study a system of hard-core boson on a one-dimensional lattice with frustrated next-nearest-neighbor hopping and nearest-neighbor interaction. At half filling, for equal magnitude of nearest- and next-nearest-neighbor hopping, the ground state of this system exhibits a first-order phase transition from a bond-ordered solid to a charge-density-wave solid as a function of the nearest-neighbor interaction. Moving away from half filling we investigate the system at incommensurate densities, where we find a supersolid phase which has concurrent off-diagonal long-range order and density-wave order which is unusual in a system of hard-core bosons in one dimension. Using the finite-size density-matrix renormalization group method, we obtain the complete phase diagram for this model.
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