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首页> 外文期刊>Physical Review. B, Condensed Matter >Edge theory approach to topological entanglement entropy, mutual information, and entanglement negativity in Chern-Simons theories
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Edge theory approach to topological entanglement entropy, mutual information, and entanglement negativity in Chern-Simons theories

机译：Chern-Simons理论中的拓扑纠缠熵，互信息和纠缠负性的边缘理论方法

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摘要

We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1 )-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus g, which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the R symbols, monodromy, and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement/correlation measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent noncontractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders.
机译：我们开发了一种基于边缘理论的方法来计算（2 + 1）维拓扑有序相中的纠缠熵和相关量。我们的方法是对例如使用复制技巧和维滕手术方法的现有方法的补充，并且适用于g属的通用空间流形，该流形可以以任意方式划分。也可以在我们的框架内直接研究Wilson线的融合和编织效果。通过考虑具有不同Wilson线构型的状态的一般叠加，通过干涉效应，我们可以通过纠缠熵检测Chern-Simons理论的拓扑数据，例如R符号，单峰和准粒子的拓扑自旋。此外，通过使用我们的方法，我们可以计算其他纠缠/相关度量，例如互信息和纠缠负性。特别是，发现圆环上两个相邻的不可收缩区域的纠缠负性提供了一种区分阿贝尔和非阿贝尔拓扑顺序的简单方法。

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  • 来源
    《Physical Review. B, Condensed Matter》 |2016年第24期|245140.1-245140.27|共27页
  • 作者

    Xueda Wen; Shunji Matsuura; Shinsei Ryu;

  • 作者单位

    Department of Phvsics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA;

    Niels Bohr International Academy and Center for Quantum Devices, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, Copenhagen, Denmark,Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan;

    Department of Phvsics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA;

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