论文标题
拓扑$ z_2 $在基塔夫旋转液体中不变：射击对称组以外的散发旋转液体的分类
Topological $Z_2$ invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group
论文作者
论文摘要
一个投影对称组（PSG）被视为旋转液体的分类理论。但是，它不包含费米尼旋子激发的对称性保护的拓扑顺序，因此间隙旋转液体的分类是不完整的。我们通过在SquareCtagon晶格上利用Kitaev模型来证明PSG以外的分类，在该晶格中，两个间隙的自旋液体由拓扑$ Z_2 $不变性区分。这个$ z_2 $不变性只能由时间反转和翻译对称性来定义，条件是时间反转对称性的情况。因此，它是具有螺旋边缘状态的一类隐藏的拓扑基塔耶式旋转液体，长期以来一直被忽略。这表明存在一个未知的分类方案，该方案是PSG以外的旋转液体。
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.
