paper

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

arXiv:cond-mat/0612227 · doi:10.1103/PhysRevB.75.214407

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.

10 pages, 12 figures. v2: Some non-trivial improvements. 1) We obtained results supporting the original KP construction (contrary to v1) and thus Sec. III-B-1 was completely rewritten. 2) An ambiguity in R was introduced for circular areas in Sec. III-A. 3) The ED result for zigzag areas was replaced due to an error in the previous version

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