Topological $Z_2$ invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group

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 squareoctagon lattice, where two gapped spin liquids are distinguished by a topological $Z_2$ invariant. This $Z_2$ 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.

arXiv comment5+2 pages, 3+1 figures, one section is moved

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Cited by in corpus (4)

• Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
• Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid
• Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields
• Entanglement entropy as a probe of topological phase transitions