AI 中文总结
研究弱拓扑如何通过解析延拓的布洛赫哈密顿量的例外奇点进行几何表述，以二维格点手征模型为例，阐述其弱拓扑不变量族，说明弱拓扑边缘态等与例外点的关系，提供了相关态的统一复动量描述。
AI 中文摘要
在本文中，我们证明了弱拓扑可以根据解析延拓的布洛赫哈密顿量的例外奇点进行几何表述。二维的一般格点手征模型作为对偶弱拓扑的最小实现，具有两个独立的弱拓扑不变量族，每个空间方向一个。弱拓扑边缘态对应于复动量空间中的例外点，而角零模则从通过复化两个动量得到的例外曲线中出现。当例外根坍缩到原点时会出现紧致局域态。该框架提供了对边缘、角和紧致局域化的统一复动量描述。
英文摘要
In this article, we demonstrate that weak topology can be formulated geometrically in terms of exceptional singularities of an analytically continued Bloch Hamiltonian. A general plaquette chiral model in two dimensions serves as a minimal realization of dual weak topology, possessing two independent families of weak topological invariants, one for each spatial direction. The weak-topological edge states correspond to exceptional points in complex momentum space, while corner zero modes emerge from exceptional curves obtained by complexifying both momenta. Compact localized states arise when the exceptional roots collapse to the origin. This framework provides a unified complex-momentum description of edge, corner, and compact localization.
Comments5 pages, 6 figures
