Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice

TL;DR

This paper numerically evaluates the topological entanglement entropy in the quantum dimer model on a triangular lattice, confirming the presence of Z_2 topological order through entanglement measures.

Contribution

It demonstrates the numerical calculation of topological entanglement entropy in a quantum dimer model, validating theoretical predictions for Z_2 topological order.

Findings

Both entanglement entropy constructions approach the expected Z_2 topological value.

Entanglement entropy on a zigzag area can serve as an alternative measurement.

Results support the presence of topological order in the model.

Abstract

A characterization of topological order in terms of bi-partite entanglement was proposed recently [A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006); M. Levin and X.-G. Wen, ibid, 110405]. It was argued that in a topological phase there is a universal additive constant in the entanglement entropy, called the topological entanglement entropy, which reflects the underlying gauge theory for the topological order. In the present paper, we evaluate numerically the topological entanglement entropy in the ground-states of a quantum dimer model on the triangular lattice, which is known to have a dimer liquid phase with Z_2 topological order. We examine the two original constructions to measure the topological entropy by combining entropies on plural areas, and we observe that in the large-area limit they both approach the value expected for Z_2 topological order. We also consider the entanglement entropy on a topologically non-trivial ``zigzag'' area and propose to use it as another way to measure the topological entropy.