Topological entanglement entropy in the quantum dimer model on the triangular lattice
Topological entanglement entropy in the quantum dimer model on the triangular lattice
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DOI：
10.1103/physrevb.75.214407
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发表时间：
2006-12
影响因子：
3.7
通讯作者：
S. Furukawa;G. Misguich
中科院分区：
文献类型：
--
作者：
S. Furukawa;G. Misguich
最近提出了一种用两粒子纠缠来刻画拓扑序的方法[A.Kitaev和J.Preskill，Phys.莱特牧师。96,110404(2006年)；M.Levin和X.-G.wen，同上，110405]。在一个拓扑阶段，纠缠熵中存在一个普遍的附加常数，称为拓扑纠缠熵，它反映了拓扑序的基本规范理论。在本文中，我们数值计算了三角形晶格上量子二聚体模型基态的拓扑纠缠熵，该模型具有Z_2拓扑级的二聚液相。我们考察了两种通过合并多个区域上的熵来度量拓扑熵的原始结构，我们观察到在大面积极限下它们都接近于Z_2拓扑序的期望值。我们还考虑了拓扑非平凡的“之字形”区域上的纠缠熵，并提出将其作为测量拓扑熵的另一种方法。
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.