Topological phase transition on the edge of two-dimensional Z2 topological order

Wei-Qiang Chen, Chao-Ming Jian, Liang Kong, Yi-Zhuang You, and Hao Zheng
Phys. Rev. B 102, 045139 – Published 23 July 2020

Abstract

The unified mathematical theory of gapped and gapless edges of two-dimensional (2d) topological orders was developed by two of the authors. According to this theory, the critical point of a purely edge topological phase transition of a 2d topological order can be mathematically characterized by an enriched fusion category. In this work, we provide a physical proof of this fact in a concrete example: the 2d Z2 topological order. In particular, we construct an enriched fusion category, which describes a gappable nonchiral gapless edge of the 2d Z2 topological order. Then, we use an explicit lattice model construction to realize a topological phase transition between the two well-known gapped edges of the 2d Z2 topological order, and show that all the ingredients of the above enriched fusion category can be realized explicitly in this lattice model.

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  • Received 10 April 2020
  • Revised 22 June 2020
  • Accepted 23 June 2020

DOI:https://doi.org/10.1103/PhysRevB.102.045139

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wei-Qiang Chen1,2,3,*, Chao-Ming Jian4,†, Liang Kong2,5,7,‡, Yi-Zhuang You6,§, and Hao Zheng2,5,7,8,∥

  • 1Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
  • 2Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 3Shenzhen Key Laboratory of Advanced Quantum Functional Materials and Devices, Southern University of Science and Technology, Shenzhen 518055, China
  • 4Kavli Institute for Theoretical Physics, University of California Santa Barbara, California 93106, USA
  • 5Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 6Department of Physics, University of California, San Diego, California 92093, USA
  • 7Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen,518055, China
  • 8Department of Mathematics, Peking University, Beijing 100871, China

  • *chenwq@sustech.edu.cn
  • cmjian@kitp.ucsb.edu
  • kongl@sustech.edu.cn
  • §yzyou@ucsd.edu
  • hzheng@math.pku.edu.cn

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Issue

Vol. 102, Iss. 4 — 15 July 2020

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