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Reduced Density Matrices and Topological Order in a Quantum Dimer Model

Shunsuke Furukawa·Gregoire Misguich·Masaki Oshikawa
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Abstract

Resonating valence bond (RVB) liquids in two dimensions are believed to exhibit topological order and to admit no local order parameter of any kind. This is a defining property of "liquids" but it has been explicitly confirmed only in a few exactly solvable models. In this paper, we investigate the quantum dimer model on the triangular lattice. It possesses an RVB-type liquid phase, however, for which the absence of a local order parameter has not been proved. We examine the question numerically with a measure based on reduced density matrices. We find a scaling of the measure which strongly supports the absence of any local order parameter.

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Shunsuke Furukawa, Gregoire Misguich, Masaki Oshikawa. 2006-12-09. Reduced Density Matrices and Topological Order in a Quantum Dimer Model. https://doi.org/10.1088/0953-8984%2F19%2F14%2F145212

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