论文标题
$ g $ - 充电的分类在1D可逆性状态
A classification of $G$-charge Thouless pumps in 1D invertible states
论文作者
论文摘要
最近，已经提出了一种理论，该理论对对称性保护拓扑（SPT）量子状态的环状过程进行了分类。对于旋转链的情况，即\ \一维玻色子SPT，该理论意味着循环过程由零维SPT进行了分类。这通常被描述为无泵的概括，原始的泵与对称组为$ u（1）$的情况相对应，并且泵由整数分类，该整数与每个周期泵送的电荷相对应。在本文中，我们在明确而严格的环境中回顾了这一一维理论，并为紧凑型对称群体$ g $的拟议分类提供了证明。
Recently, a theory has been proposed that classifies cyclic processes of symmetry protected topological (SPT) quantum states. For the case of spin chains, i.e.\ one-dimensional bosonic SPT's, this theory implies that cyclic processes are classified by zero-dimensional SPT's. This is often described as a generalization of Thouless pumps, with the original Thouless pump corresponding to the case where the symmetry group is $U(1)$ and pumps are classified by an integer that corresponds to the charge pumped per cycle. In this paper, we review this one-dimensional theory in an explicit and rigorous setting and we provide a proof for the completeness of the proposed classification for compact symmetry groups $G$.
