Topological Z2 invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group
Masahiko G. Yamada
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 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:2005.03399•Physical Review Research•Jan 4, 2021•12 citations