一维链的拓扑边态及指标理论

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-03-16 DOI:10.1063/5.0150870

Guo Chuan Thiang

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引用次数: 0

摘要

我们提供了一个著名的物理学思想的基本证明和改进:半空间上的手性对称局部哈密顿量具有与其体圈数相同的体带隙中具有能量的边缘局域态的符号数。强调了将一般和非一般情况联系起来的非基本方法的要求。我们的动手方法补充了基于Toeplitz算子的经典指标理论的快速抽象证明。

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Topological edge states of 1D chains and index theory

We provide an elementary proof and refinement of a well-known idea from physics: a chiral-symmetric local Hamiltonian on a half-space has the same signed number of edge-localized states with energies in the bulk bandgap as its bulk winding number. The requirement of non-elementary methods to relate generic and non-generic cases is emphasized. Our hands-on approach complements a quick abstract proof based on the classical index theory of Toeplitz operators.

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来源期刊

Journal of Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.