Negativity and topological order in the toric code
Negativity and topological order in the toric code
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DOI：
10.1103/physreva.88.042319
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发表时间：
2013-10-16
影响因子：
2.9
通讯作者：
Castelnovo, C.
中科院分区：
文献类型：
--
作者：
Castelnovo, C.
在本文中，我们研究的纠缠措施被称为负的情况下，环面代码模型的行为。使用最近由Calabrese，Cardy和Tonni [Phys. Rev. Lett. 109，130502（2012）]，我们得到了一个精确的表达式，它说明了存在于拓扑有序状态中的非局部相关性如何反映在系统的负性行为中。我们发现，负性有一个领先的面积法的贡献，如果子系统是直接接触彼此（如预期在零范围相关模型）。我们还发现了拓扑贡献直接相关的拓扑熵，只要分区是拓扑非平凡的两个方向上的环面。我们进一步确认，通过明确的计算，负捕获量子纠缠的贡献。事实上，我们表明，负消失相同的经典拓扑有序八顶点模型，相反，表现出有限的冯诺依曼熵，包括拓扑校正。
In this paper we study the behavior of the entanglement measure dubbed negativity in the context of the toric code model. Using a replica method introduced recently by Calabrese, Cardy, and Tonni [Phys. Rev. Lett. 109, 130502 (2012)], we obtain an exact expression which illustrates how the nonlocal correlations present in a topologically ordered state reflect in the behavior of the negativity of the system. We find that the negativity has a leading area-law contribution if the subsystems are in direct contact with one another (as expected in a zero-range correlated model). We also find a topological contribution directly related to the topological entropy, provided that the partitions are topologically nontrivial in both directions on a torus. We further confirm by explicit calculation that the negativity captures only quantum contributions to the entanglement. Indeed, we show that the negativity vanishes identically for the classical topologically ordered eight-vertex model, which on the contrary exhibits a finite von Neumann entropy, inclusive of topological correction.