Topological entanglement entropy
Topological entanglement entropy
复制标题
DOI：
10.1103/physrevlett.96.110404
复制
发表时间：
2006-03-24
影响因子：
8.6
通讯作者：
Preskill, J
中科院分区：
文献类型：
--
作者：
Kitaev, A;Preskill, J
我们给出了具有质量隙的二维拓扑有序介质基态中多粒子量子纠缠的普适刻画。我们考虑一个平面上的圆盘，其光滑边界的长度为L，与相关长度相比较大。在基态下，通过追踪圆盘外部的所有自由度，我们得到了内部自由度的边际密度算符ρ。rho的冯诺依曼熵，内部和外部变量纠缠的度量，具有S（rho）=alpha L-gamma+.的形式，其中省略号表示在极限L ->无穷大中消失的项。我们表明，γ是一个普遍的常数表征的全球性的纠缠在基态。利用拓扑量子场论的方法，我们推导出一个公式的伽马在超选择部门的介质的属性。
We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho)=alpha L-gamma+..., where the ellipsis represents terms that vanish in the limit L ->infinity. We show that -gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.