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  • Letter
  • Open Access

Topological Z2 invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group

Masahiko G. Yamada*

  • Department of Materials Engineering Science, Osaka University, Toyonaka 560-8531, Japan and Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan

  • *myamada@mp.es.osaka-u.ac.jp
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Phys. Rev. Research 3, L012001 – Published 4 January, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012001

Abstract

A projective symmetry group (PSG) has been regarded as a classification theory of spin liquids. However, it does not include a symmetry-protected topological order of fermionic spinon excitations, and thus the classification of gapped spin liquids is incomplete. We demonstrate the classification beyond PSG by utilizing the Kitaev model on the square-octagon lattice, where two gapped spin liquids are distinguished by a topological Z2 invariant. This Z2 invariant can be defined solely by the time-reversal and translation symmetries on condition that the time-reversal symmetry is implemented projectively. Thus, it is a hidden class of topological Kitaev spin liquids with helical edge states, which has been ignored for a long time. This suggests that there exists an unknown classification scheme of gapped spin liquids beyond PSG.

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Phys. Rev. Research 3, L012001– Published 4 January, 2021
  • Received 8 May 2020
  • Accepted 8 December 2020
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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