Title: Topological phases of non-interacting systems: A general approach based on states Show Chinese title

Title: 非相互作用系统的拓扑相：基于态的一般方法

Abstract: In this work we provide a classification scheme for topological phases of certain systems whose observable algebra is described by a trivial $C^*$-bundles. The classification is based on the study of the homotopy classes of \emph{configurations}, which are maps from a \emph{quantum parameter space} to the space of pure states of a reference \emph{fiber} $C^*$-algebra. Both the quantum parameter space and the fiber algebra are naturally associated with the observable algebra. A list of various examples described in the last section shows that the common classification scheme of non-interacting topological insulators of type A is recovered inside this new formalism. Show Chinese abstract

Abstract: 在本工作中，我们提供了一种分类方案，用于某些系统的拓扑相，其可观测代数由平凡的$C^*$-丛描述。 该分类基于对\emph{配置}的同伦类的研究，这些同伦类是从\emph{量子参数空间}到参考\emph{纤维} $C^*$ -代数的纯态空间的映射。 量子参数空间和纤维代数都自然地与可观测代数相关联。 最后一节中列出的各种示例表明，非相互作用拓扑绝缘体类型 A 的常见分类方案在此新形式主义中被恢复。