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Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I

  • Jiaqi LouEmail author
  • Ce Shen
  • Ling-Yan Hung
Open Access
Regular Article - Theoretical Physics
  • 41 Downloads

Abstract

In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic topological order and investigate how the topological entanglement entropy is sensitive to them. We present a detailed analysis of the Ishibashi states describing these edges/interfaces making use of the physics of anyon condensation in the context of Abelian Chern-Simons theory, which is then generalized to more non-Abelian theories whose edge RCFTs are known. Then we apply these results to computing the entanglement entropy of different topological orders. We consider cases where the system resides on a cylinder with gapped boundaries and that the entanglement cut is parallel to the boundary. We also consider cases where the entanglement cut coincides with the interface on a cylinder. In either cases, we find that the topological entanglement entropy is determined by the anyon condensation pattern that characterizes the interface/boundary. We note that conditions are imposed on some non-universal parameters in the edge theory to ensure existence of the conformal interface, analogous to requiring rational ratios of radii of compact bosons.

Keywords

Anyons Chern-Simons Theories Conformal Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Surface PhysicsFudan UniversityShanghaiChina
  2. 2.Collaborative Innovation Center of Advanced MicrostructuresNanjingChina
  3. 3.Department of Physics and Center for Field Theory and Particle PhysicsFudan UniversityShanghaiChina
  4. 4.Institute for Nanoelectronic devices and Quantum computingFudan UniversityShanghaiChina

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