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arXiv:0809.1667 · Physical Review Letters

Extended Supersolid Phase of Frustrated Hard-Core Bosons on a Triangular Lattice

Fa Wang, Frank Pollmann, Ashvin Vishwanath

Published Jan 5, 2009• 64 citations
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Abstract

We study a model of hard-core bosons with frustrated nearest-neighbor hopping (t) and repulsion (V) on the triangular lattice. We argue for a supersolid ground state in the large repulsion (V>>|t|) limit where a dimer representation applies, by constructing a unitary mapping to the well-understood unfrustrated hopping case. This generalized "Marshall sign rule" allows us to establish the precise nature of the supersolid order by utilizing a recently proposed dimer variational wave function, whose correlations can be efficiently calculated using the Grassmann approach. By continuity, a supersolid is predicted over the wide parameter range, V>-2t>0. This also establishes a simple phase diagram for the triangular lattice spin 1/2 XXZ antiferromagnet.

DOI
10.1103/physrevlett.102.017203

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We study a model of hard-core bosons with frustrated nearest-neighbor hopping (t) and repulsion (V) on the triangular lattice. We argue for a supersolid ground state in the large repulsion (V>>|t|) limit where a dimer representation applies, by constructing a unitary mapping to the well-understood unfrustrated hopping case. This generalized "Marshall sign rule" allows us to establish the precise nature of the supersolid order by utilizing a recently proposed dimer variational wave function, whose correlations can be efficiently calculated using the Grassmann approach. By continuity, a supersolid is predicted over the wide parameter range, V>-2t>0. This also establishes a simple phase diagram for the triangular lattice spin 1/2 XXZ antiferromagnet.
We numerically demonstrate that a supersolid phase exists in a frustrated hard-core boson system on a triangular lattice over a wide range of interaction strength. In the infinite repulsion (Ising) limit, we establish a mapping to the same problem with unfrustrated hopping, which connects the supersolid to the known results in that case. The weak superfluidity can be destroyed or strongly enhanced by a next-nearest-neighbor hopping term, which provides valuable information for experimental realization of a supersolid phase on optical lattice. A phase diagram for the frustrated anisotropic Heisenberg model on triangular lattice is also established.
We study hard-core bosons with unfrustrated hopping (t) and nearest neighbor repulsion (U) (spin S=1/2 XXZ model) on the triangular lattice. At half filling, the system undergoes a zero temperature (T) quantum phase transition from a superfluid phase at small U to a supersolid at Uc approximately 4.45 in units of 2t. This supersolid phase breaks the lattice translation symmetry in a characteristic sqrt[3] x square root of 3 pattern, and is remarkably stable--indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large U/t.
Hard-core bosons on a triangular lattice with nearest-neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.
We investigate the interplay between commensurate lock-in and incommensurate supersolid phases of the hard-core bosons at half-filling with anisotropic nearest-neighbor hopping and repulsive interactions on triangular lattice. We use numerical quantum and variational Monte Carlo as well as analytical Schwinger boson mean-field analysis to establish the ground states and phase diagram. It is shown that, for finite-size systems, there exist a series of jumps between different supersolid phases as the anisotropy parameter is changed. The density ordering wave vectors are locked to commensurate values and jump between adjacent supersolids. In the thermodynamic limit, however, the magnitude of these jumps vanishes leading to a continuous set of novel incommensurate supersolid phases.
We study the boson model on a triangular lattice interacting only via on-site hardcore repulsion by mapping to a system of spins (S=1/2)(S = 1/2)(S=1/2). We investigate the supersolid phase of the systems which is a state matter displaying both diagonal long- range (solid) order as well as off-diagonal long-range (superfluidity) by utilizing a semionic representation for the spin-XXZ model. We show that the supersolid order is stable in the mean-field theory for a broad region of parameters. The inclusion of spin wave corrections modifies this picture, but the supersolid phase is still quite robust on the triangular lattices.