Ground-state properties of the Rokhsar-Kivelson dimer model on the triangular lattice

TL;DR

This paper demonstrates that the Rokhsar-Kivelson dimer model on the triangular lattice exhibits topological quantum liquid behavior, with exponentially decaying differences in local properties between degenerate ground states, indicating topological order.

Contribution

It provides a rigorous proof of topological order in the model using Pfaffian techniques and relates correlation lengths of local and vison operators.

Findings

Difference in local properties decays exponentially with system size

Correlation length equals that of the vison operator

Model exhibits topological quantum liquid behavior

Abstract

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 the system size. We compute the relevant correlation length and show that it equals the correlation length of the vison operator.