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Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks

Yu-Hsueh Chen1, Ching-Yu Huang2,*, and Ying-Jer Kao1,†

  • 1Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei 10607, Taiwan
  • 2Department of Applied Physics, Tunghai University, Taichung 40704, Taiwan

  • *cyhuangphy@thu.edu.tw
  • †yjkao@phys.ntu.edu.tw
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Phys. Rev. B 104, 045131 – Published 20 July, 2021

DOI: https://doi.org/10.1103/PhysRevB.104.045131

Abstract

We propose a unified scheme to identify phase transitions out of the Z2 Abelian topological order, including the transition to a non-Abelian chiral spin liquid. Using loop gas and and string gas states [H.-Y. Lee, R. Kaneko, T. Okubo, and N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)] on the star lattice Kitaev model as an example, we compute the overlap of minimally entangled states through transfer matrices. We demonstrate that, similar to the anyon condensation, continuous deformation of a Z2-injective projected entangled-pair state (PEPS) also allows us to study the transition between Abelian and non-Abelian topological orders. We show that the charge and flux anyons defined in the Abelian phase transmute into the σ anyon in the non-Abelian topological order. Furthermore, we show that contrary to the claim in [Phys. Rev. B 101, 035140 (2020)], both the LG and SG states have infinite correlation length in the non-Abelian regime, consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian.

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Phys. Rev. B 104, 045131– Published 20 July, 2021
  • Received 4 March 2021
  • Revised 2 July 2021
  • Accepted 6 July 2021
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