Reduced Density Matrices and Topological Order in a Quantum Dimer Model

TL;DR

This paper investigates the quantum dimer model on a triangular lattice, providing numerical evidence that supports the absence of local order parameters in the RVB-type liquid phase, indicating topological order.

Contribution

It introduces a numerical measure based on reduced density matrices to analyze topological order in the quantum dimer model, confirming the liquid phase's non-local nature.

Findings

The measure scales consistently with the absence of local order parameters.

Numerical results support the topological nature of the RVB liquid phase.

Provides evidence for topological order in a non-exactly solvable 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.