A Z_2-index of Symmetry Protected Topological Phases with Reflection Symmetry for Quantum Spin Chains
A Z_2-index of Symmetry Protected Topological Phases with Reflection Symmetry for Quantum Spin Chains
复制标题
量子自旋链具有反射对称性的对称保护拓扑相的Z_2指数
DOI：
10.1007/s00220-021-04057-3
复制
发表时间：
2021
影响因子：
2.4
通讯作者：
Ogata Yoshiko
中科院分区：
文献类型：
--
作者：
Naaijkens Pieter;Ogata Yoshiko;Ogata Yoshiko;Ogata Yoshiko;Ogata Yoshiko
对于SPT阶段的分类，确定一个指数是一个中心问题。在著名的论文（Pollmann et al. Phys Rev B 81：064439，2010）中，Pollmann、Tuner、贝格和Oshikawa引入了具有二面体群（关于x、y和z轴的旋转）对称性、时间反演对称性或反射对称性的内射矩阵乘积态的指数。前两个是现场对称性。在绪方在A-指数的对称性保护的拓扑相位与时间反演对称的量子自旋链。 1810.01045 在量子自旋链中引入了一个用于在位对称性的指数，它推广了Pollmann等人（2010）中的指数，用于量子自旋链中的一般唯一带隙基态相。证明了该指数是SPT相位分类的不变量。反射对称性的指数，这不是一个现场的对称性，是一个悬而未决的问题。本文引入了反射对称唯一带隙基态相位的α-指数，完成了Pollmann等人关于指数的推广问题，并证明了该指数是α-分类的不变量.
For the classification of SPT phases, defining an index is a central problem. In the famous paper (Pollmann et al. Phys Rev B 81:064439, 2010), Pollmann, Tuner, Berg, and Oshikawa introduced-indices for injective matrix products states which have eitherdihedral group (of-rotations aboutx,y, andz-axes) symmetry, time-reversal symmetry, or reflection symmetry. The first two are on-site symmetries. In Ogata in A-index of symmetry protected topological phases with time reversal symmetry for quantum spin chains. arXiv:1810.01045 , an index for on-site symmetries, which generalizes the index in Pollmann et al. (2010), was introduced for general unique gapped ground state phases in quantum spin chains. It was proved that the index is an invariant of the-classification of SPT phases. The index for the reflection symmetry, which is not an on-site symmetry, was left as an open question. In this paper, we introduce a-index for the reflection symmetric unique gapped ground state phases, and complete the generalization problem of index by Pollmann et al. We also show that the index is an invariant of the-classification.