论文标题
一维对称阶段受到饰面对称性
One-dimensional symmetric phases protected by frieze symmetries
论文作者
论文摘要
我们对使用矩阵产品状态在一个维度中的frieze空间组的存在下对量子旋转链的对称保护拓扑链进行系统研究。在这里，考虑一维晶格的空间对称性与额外的“垂直反射”一起考虑，我们将其作为现场$ \ mathbb {z} _2 _2 $对称性。我们确定了十七个不同的非平凡阶段，定义了规范形式，并比较了从MPS分析获得的拓扑指数与组的共同体预测。我们此外，构造具有全局现场对称性的对称性保护拓扑阶段的显式重新归一化组固定点波函数，可能与时间反向和平均对称性结合在一起。在途中，我们演示了如何使用史密斯正常形式计算群体的同胞。
We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional lattice are considered together with an additional 'vertical reflection', which we take to be an on-site $\mathbb{Z}_2$ symmetry. We identify seventeen distinct non-trivial phases, define canonical forms, and compare the topological indices obtained from the MPS analysis with the group cohomological predictions. We furthermore construct explicit renormalization group fixed-point wave functions for symmetry-protected topological phases with global on-site symmetries, possibly combined with time-reversal and parity symmetry. En route, we demonstrate how group cohomology can be computed using the Smith normal form.
