论文标题
一维费米昂系统的对称受保护拓扑阶段的分类
The classification of symmetry protected topological phases of one-dimensional fermion systems
论文作者
论文摘要
我们引入了一个无限式费米子链的对称性保护拓扑（SPT）阶段的索引，并具有有限组$ g $的现场对称性。该索引在$ \ mathbb {z} _2 \ times h^1（g，\ mathbb {z} _2）\ times h^2（g，u（u（1）_ {\ mathfrak {p}}}）$带有stacking的一般性墙集团定律。我们表明该指数是SPT阶段分类的不变性。当基态是翻译不变的，并且在有限间隔内降低了均匀边界等级的密度矩阵时，我们将带有现场对称性的代表该状态的费米子矩阵乘积。
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.
