### Abstract

A characterization of topological order in terms of bi-partite entanglement was proposed recently. 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 Z2 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 Z2 topological order. We also consider the entanglement entropy on a topologically nontrivial "zigzag" area and propose to use it as another way to measure the topological entropy.

Original language | English |
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Article number | 214407 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 75 |

Issue number | 21 |

DOIs | |

Publication status | Published - 2007 Jun 5 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

**Topological entanglement entropy in the quantum dimer model on the triangular lattice.** / Furukawa, Shunsuke; Misguich, Grégoire.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 75, no. 21, 214407. https://doi.org/10.1103/PhysRevB.75.214407

}

TY - JOUR

T1 - Topological entanglement entropy in the quantum dimer model on the triangular lattice

AU - Furukawa, Shunsuke

AU - Misguich, Grégoire

PY - 2007/6/5

Y1 - 2007/6/5

N2 - A characterization of topological order in terms of bi-partite entanglement was proposed recently. 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 Z2 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 Z2 topological order. We also consider the entanglement entropy on a topologically nontrivial "zigzag" area and propose to use it as another way to measure the topological entropy.

AB - A characterization of topological order in terms of bi-partite entanglement was proposed recently. 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 Z2 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 Z2 topological order. We also consider the entanglement entropy on a topologically nontrivial "zigzag" area and propose to use it as another way to measure the topological entropy.

UR - http://www.scopus.com/inward/record.url?scp=34347407227&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34347407227&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.75.214407

DO - 10.1103/PhysRevB.75.214407

M3 - Article

VL - 75

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 21

M1 - 214407

ER -