标题： 绝缘体的拓扑分类：I. 非相互作用带隙一维系统 显示英文标题

标题： Topological Classification of Insulators: I. Non-interacting Spectrally-Gapped One-Dimensional Systems

摘要： 我们研究了一维无序材料中的非相互作用电子，这些材料表现出能隙，并且属于Altland-Zirnbauer对称性类的十种类型之一。 我们在哈密顿量空间上定义了一个适当的拓扑结构，使得所谓的强拓扑不变量成为完全不变量，从而得到Kitaev周期表的一维列，但这次推导不依赖于K理论。 因此，我们证实了关于带隙非相互作用一维系统中的拓扑相与谱隙区域的相应阿贝尔群 $\{0\},\mathbb{Z},2\mathbb{Z},\mathbb{Z}_2$ 之间存在一一对应关系的猜想。 我们发展的主要工具是一种关于局域么正算子和正交投影的等变同伦理论。 此外，我们讨论了将么正理论扩展到部分等距算子，以提供理解强无序、迁移率带隙材料的视角。 显示英文摘要

摘要： We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the so-called strong topological invariants become complete invariants yielding the one-dimensional column of the Kitaev periodic table, but now derived without recourse to K-theory. We thus confirm the conjecture regarding a one-to-one correspondence between topological phases of gapped non-interacting 1D systems and the respective Abelian groups $\{0\},\mathbb{Z},2\mathbb{Z},\mathbb{Z}_2$ in the spectral gap regime. The main tool we develop is an equivariant theory of homotopies of local unitaries and orthogonal projections. Moreover, we discuss an extension of the unitary theory to partial isometries, to provide a perspective towards the understanding of strongly-disordered, mobility-gapped materials.