Reduced Density Matrices and Topological Order in a Quantum Dimer Model

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.

6 pages, 3 figures. To appear in J. Phys.: Condens. Matter (Proceedings of "Highly Frustrated Magnets", Osaka (Japan), August 2006). Version 2: improved figures containing new data and minor changes in the text

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• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems
• Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity
• Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems
• Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation