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 |
|---|---|
| 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.
In: Physical Review B - Condensed Matter and Materials Physics, Vol. 75, No. 21, 214407, 05.06.2007.Research output: Contribution to journal › Article
}
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.
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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 -