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This theoretical investigation reveals topological order in a liquid phase of the Rokhsar-Kivelson dimer model on a triangular lattice, suggesting key properties of the system.
We explicitly show that the Rokhsar-Kivelson dimer model on the triangular lattice is a liquid with topological order. Using the Pfaffian technique, we prove that the difference in local properties between the two topologically degenerate ground states on the cylinders and on the tori decreases exponentially with increasing system size. We compute the relevant correlation length and show that it equals the correlation length of the vison operator.
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Ioselevich et al. (2002) studied this question.
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