Edge theory approach to topological entanglement entropy, mutual information, and entanglement negativity in Chern-Simons theories

Xueda Wen, Shunji Matsuura, Shinsei Ryu

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49 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number245140
JournalPhysical Review B
Volume93
Issue number24
DOIs
StatePublished - Jun 20 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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