{"title":"Topological edge states of 1D chains and index theory","authors":"Guo Chuan Thiang","doi":"10.1063/5.0150870","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"88 6 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics Analysis Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0150870","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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