Non-Hermitian topological systems exhibit properties very different from those of their Hermitian counterparts. An important puzzling issue for non-Hermitian topological systems is the existence of defective edge states beyond the usual bulk-boundary correspondence (BBC). In this Rapid Communication, to understand the existence of these defective edge states, the number-anomalous bulk-boundary correspondence (NA-BBC) theory, which distinguishes the non-Bloch BBC, is developed. With the one-dimensional non-Hermitian Su-Schrieffer-Heeger model taken as an example, the underlying physics of the defective edge states is explored. The defective edge states are a consequence of non-Hermitian coalescence from the anomalous edge Hamiltonian. In addition, with the help of a theorem, the number anomaly of the edge states in non-Hermitian topological systems becomes a mathematical problem in quantitative calculations when identifying the normal/non-normal non-Hermitian condition for the edge Hamiltonian and verifying the deviation of the BBC ratio from 1. In the future, NA-BBC theory can be generalized to higher-dimensional non-Hermitian topological systems (for example, the two-dimensional Chern insulator).

中文翻译：

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非Hermitian拓扑系统中的缺陷边缘状态和数量异常的体边界对应

非Hermitian拓扑系统表现出的特性与Hermitian对应系统的特性截然不同。对于非Hermitian拓扑系统来说，一个重要的令人困惑的问题是，边缘边缘状态的缺陷超出了通常的体边界对应（BBC）。在本快速通信中，为了理解这些缺陷边缘状态的存在，发展了区分非Bloch BBC的数异常体边界对应（NA-BBC）理论。以一维非Hermitian Su-Schrieffer-Heeger模型为例，探讨了缺陷边缘态的基本物理性质。缺陷边缘状态是由于异常边缘哈密顿量引起的非埃尔米特合并的结果。此外，借助一个定理，