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Topological edge states of 1D chains and index theory

Guo Chuan Thiang
Mar 2023
摘要
We provide an elementary proof and refinement of a well-known idea fromphysics: a chiral-symmetric local Hamiltonian on a half-space has the samesigned number of edge-localized states with energies in the bulk band gap, asits bulk winding number. The requirement of non-elementary methods to relategeneric and non-generic cases is emphasized. Our hands-on approach complementsa quick abstract proof based on the classical index theory of Toeplitzoperators.
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