拓扑相：同构、同伦与$K$ -理论
Topological phases: isomorphism, homotopy and $K$-theory
摘要：
与给定的对称性约束相容的带隙哈密顿算子的等价类，例如那些潜在的拓扑绝缘体，可以用许多方式定义。对于布里渊环面上的矢量丛模型的非手征类，物理相关的等价包括同构，同伦，和$K$ -理论，这是不等价的，但密切相关。我们讨论了一个重要的微妙之处，出现在手征类AIII系统，其中的缠绕数不变量被证明是相对的，而不是绝对的，因为通常假设。这些问题，然后分析和调和的语言$K$理论。
英文摘要：
Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modelled by vector bundles over Brillouin tori, physically relevant equivalences include isomorphism, homotopy, and $K$-theory, which are inequivalent but closely related. We discuss an important subtlety which arises in the chiral Class AIII systems, where the winding number invariant is shown to be relative rather than absolute as is usually assumed. These issues are then analyzed and reconciled in the language of $K$-theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
