标题： 局部等价的准自由态与指标理论 显示英文标题

标题： Locally equivalent quasifree states and index theory

摘要： 我们从指标理论和对称保护拓扑(SPT)相的观点出发，考虑阿基的自对偶CAR代数的准自由基态。 我们首先回顾如何通过Clifford模指标来表征连接对称能隙基态的拓扑障碍。 然后将此构造推广，以在$KO_\ast(A^\mathfrak{r})$中给出不变量，其中$A$是允许变形的$C^{*,\mathfrak{r}}$-代数。 当$A=C^*(X)$时，即粗空间$X$的Roe代数，并且我们限制在与相对于$X$局部等价的能隙基态时，还构造了一个$K$-同调类。 粗略汇合映射将这两个类相关联，并阐明了$K$-同调与自由费米子SPT相的相关性。 显示英文摘要

摘要： We consider quasifree ground states of Araki's self-dual CAR algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Clifford module indices characterise a topological obstruction to connect pairs of symmetric gapped ground states. This construction is then generalised to give invariants in $KO_\ast(A^\mathfrak{r})$ with $A$ a $C^{*,\mathfrak{r}}$-algebra of allowed deformations. When $A=C^*(X)$, the Roe algebra of a coarse space $X$, and we restrict to gapped ground states that are locally equivalent with respect $X$, a $K$-homology class is also constructed. The coarse assembly map relates these two classes and clarifies the relevance of $K$-homology to free-fermionic SPT phases.