论文标题
a $ \ mathbb {z} _ {2} $ - 无准费米子的拓扑索引
A $\mathbb{Z}_{2}$-Topological Index for Quasi-Free Fermions
论文作者
论文摘要
我们使用无限的尺寸自dual $ \ mathrm {car} $ $ c^{*} $ - 代数来研究$ \ mathbb {z} _ {2} $ - 索引，该索引分类，该索引分类了嵌入在$ \ mathbb {z}^d} $ dients $ dise的自由式系统。 Combes-thomas估计值是表明$ \ mathbb {z} _ {2} $ - 索引相对于系统大小均匀的。我们还处理一组基础状态，以完全描述基础系统的数学结构。此外，弱$^{*} $ - 线性函数集的拓扑用于分析连接不同接地状态集的路径。
We use infinite dimensional self-dual $\mathrm{CAR}$ $C^{*}$-algebras to study a $\mathbb{Z}_{2}$-index, which classifies free-fermion systems embedded on $\mathbb{Z}^{d}$ disordered lattices. Combes-Thomas estimates are pivotal to show that the $\mathbb{Z}_{2}$-index is uniform with respect to the size of the system. We additionally deal with the set of ground states to completely describe the mathematical structure of the underlying system. Furthermore, the weak$^{*}$-topology of the set of linear functionals is used to analyze paths connecting different sets of ground states.
