Reduced density matrices and topological order in a quantum dimer model

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 confirmed explicitly only in a few exactly solvable models. In this paper, we investigate the quantum dimer model on the triangular lattice. This 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.