Correspondence between bulk entanglement and boundary excitation spectra in two-dimensional gapped topological phases

Zhu-Xi Luo, Brendan G. Pankovich, Yuting Hu, and Yong-Shi Wu
Phys. Rev. B 99, 205137 – Published 22 May 2019

Abstract

We study the correspondence between boundary excitation distribution spectrum of nonchiral topological orders on an open surface M with gapped boundaries and the entanglement spectrum in the bulk of gapped topological orders on a closed surface. The closed surface is bipartitioned into two subsystems, one of which has the same topology as M. Specifically, we focus on the case of generalized string-net models and discuss the cases where M is a disk or a cylinder. When M has the topology of a cylinder, different combinations of boundary conditions of the cylinder will correspond to different entanglement cuts on the torus. When both boundaries are charge (smooth) boundaries, the entanglement spectrum can be identified with the boundary excitation distribution spectrum at infinite temperature and constant fugacities. Examples of toric code, ZN theories, and the simple non-Abelian case of doubled Fibonacci are demonstrated.

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  • Received 20 March 2019
  • Revised 7 May 2019

DOI:https://doi.org/10.1103/PhysRevB.99.205137

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhu-Xi Luo1,*, Brendan G. Pankovich1, Yuting Hu2,3, and Yong-Shi Wu4,5,6,1,†

  • 1Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
  • 2Department of Physics and Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 3CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 4State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
  • 5Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China
  • 6Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, China

  • *Corresponding author: zhuxi.luo@utah.edu
  • Corresponding author: yswu@fudan.edu.cn

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Issue

Vol. 99, Iss. 20 — 15 May 2019

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