近日，香港科技大学的Che Ting Chan及Hongwei Jia课题组与南方科技大学的朱一飞等人合作并取得一项新进展。经过不懈努力，他们发现非厄米燕尾突变揭示了不同拓扑奇点间跃迁。相关研究成果已于2023年5月4日在国际知名学术期刊《自然—物理学》上发表。

该研究团队报道了一种结构丰富的简并形态，称为奇异理论中的燕尾突变，它可以在具有宇称-时间和赝厄米对称性的非厄米系统中自然存在。燕尾包含三种不同类型的奇点，即孤立的节点线、一对三阶异常线和非缺陷交点线，它们同时存在并相互作用。虽然这些奇点看起来是独立的，但它们通过燕尾的顶点稳定地连接在一个点上，通过这个点可以发生跃迁。研究人员在一个非互易电路中实现了这样的系统，并实验观察了燕尾的简并特征。通过对本征态的框架旋转和变形进行研究，研究人员进一步证明了各种跃迁是受到拓扑保护的。

据介绍，非厄米系统中的奇异点是一种独特的特征，其特点是哈密顿量的本征值和相应的本征态会在某些特定位置融合在一起。这些奇异点的拓扑结构会导致许多引人入胜的物理现象，例如体积费米弧和本征值编织。

附：英文原文

Title: Non-Hermitian swallowtail catastrophe revealing transitions among diverse topological singularities

Author: Hu, Jing, Zhang, Ruo-Yang, Wang, Yixiao, Ouyang, Xiaoping, Zhu, Yifei, Jia, Hongwei, Chan, Che Ting

Issue&Volume: 2023-05-04

Abstract: Exceptional points are a unique feature of non-Hermitian systems at which the eigenvalues and corresponding eigenstates of a Hamiltonian coalesce. Many intriguing physical phenomena arise from the topology of exceptional points, such as bulk Fermi arcs and the braiding of eigenvalues. Here we report that a structurally richer degeneracy morphology, known as the swallowtail catastrophe in singularity theory, can naturally exist in non-Hermitian systems with both parity–time and pseudo-Hermitian symmetries. For the swallowtail, three different types of singularity exist at the same time and interact with each other—an isolated nodal line, a pair of exceptional lines of order three and a non-defective intersection line. Although these singularities seem independent, they are stably connected at a single point—the vertex of the swallowtail—through which transitions can occur. We implement such a system in a non-reciprocal circuit and experimentally observe the degeneracy features of the swallowtail. Based on the frame rotation and deformation of eigenstates, we further demonstrate that the various transitions are topologically protected.

DOI: 10.1038/s41567-023-02048-w

Source: https://www.nature.com/articles/s41567-023-02048-w