一维费米子系统对称保护拓扑相的分类
The classification of symmetry protected topological phases of one-dimensional fermion systems
摘要：
引入了一个在格对称性由有限群$G$给出的无限费米子链的对称性保护拓扑相指数。该指数取$\mathbb{Z}_2 \times H^1(G,\mathbb{Z}_2) \times H^2(G, U(1)_{\mathfrak{p}})$中的值，在堆叠下具有广义的壁群定律。我们表明，这个指数是一个不变量的SPT阶段的分类。当基态是平移不变的，并具有约化的密度矩阵与一致有界的秩在有限的时间间隔，我们推导出一个费米子矩阵乘积表示这种状态与现场对称性。
英文摘要：
We introduce an index for symmetry protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group $G$. This index takes values in $\mathbb{Z}_2 \times H^1(G,\mathbb{Z}_2) \times H^2(G, U(1)_{\mathfrak{p}})$ with a generalized Wall group law under stacking. We show that this index is an invariant of the classification of SPT phases. When the ground state is translation invariant and has reduced density matrices with uniformly bounded rank on finite intervals, we derive a fermionic matrix product representative of this state with on-site symmetry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
