中国物理B ›› 2026, Vol. 35 ›› Issue (1): 10203-010203.doi: 10.1088/1674-1056/ae2265

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Exceptional point-induced knot structure transformations in non-Abelian braids

Lin-Sheng Bao(包淋升)1, Jia-Yun Ning(宁佳运)1, Ao-Qian Shi(史奥芊)1, Peng Peng(彭鹏)1, Zhen-Nan Wang(王瑱男)1, Chao Peng(彭超)2, Shuang-Chun Wen(文双春)1, and Jian-Jun Liu(刘建军)1,3,†   

  1. 1 Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, Changsha 410082, China;
    2 State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics & Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China;
    3 Greater Bay Area Institute for Innovation, Hunan University, Guangzhou 511300, China
  • 收稿日期:2025-10-16 修回日期:2025-11-19 接受日期:2025-11-21 发布日期:2025-12-30
  • 通讯作者: Jian-Jun Liu E-mail:jianjun.liu@hnu.edu.cn
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China (Grant Nos. 62575099, 62075059, and 61405058), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2024A1515011353), Open Project of the State Key Laboratory of Advanced Optical Communication Systems and Networks of China (Grant No. 2024GZKF20), the Natural Science Foundation of Hunan Province (Grant Nos. 2020JJ4161 and 2017JJ2048), and Scientific Research Foundation of Hunan Provincial Education Department (Grant No. 21A0013).

Exceptional point-induced knot structure transformations in non-Abelian braids

Lin-Sheng Bao(包淋升)1, Jia-Yun Ning(宁佳运)1, Ao-Qian Shi(史奥芊)1, Peng Peng(彭鹏)1, Zhen-Nan Wang(王瑱男)1, Chao Peng(彭超)2, Shuang-Chun Wen(文双春)1, and Jian-Jun Liu(刘建军)1,3,†   

  1. 1 Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, Changsha 410082, China;
    2 State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics & Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China;
    3 Greater Bay Area Institute for Innovation, Hunan University, Guangzhou 511300, China
  • Received:2025-10-16 Revised:2025-11-19 Accepted:2025-11-21 Published:2025-12-30
  • Contact: Jian-Jun Liu E-mail:jianjun.liu@hnu.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (Grant Nos. 62575099, 62075059, and 61405058), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2024A1515011353), Open Project of the State Key Laboratory of Advanced Optical Communication Systems and Networks of China (Grant No. 2024GZKF20), the Natural Science Foundation of Hunan Province (Grant Nos. 2020JJ4161 and 2017JJ2048), and Scientific Research Foundation of Hunan Provincial Education Department (Grant No. 21A0013).

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摘要： The strong connection between braids and knots provides valuable insights into studying the topological state and phase classification of various physical systems. The phenomenon of non-Hermitian (NH) two- and three-band braiding has received widespread attention. However, a systematic exploration and visualization of non-Abelian braiding and the associated knot transformations in four-band systems remains unexplored. Here, we propose a theoretical model of NH four-band braiding, provide its phase diagram, and establish its trivial, Abelian, and non-Abelian braiding rules. Additionally, we report on special knots, such as the Hopf and Solomon links in braided knots, and reveal that their transformations are accompanied by and mediated through exceptional points. Our work provides a detailed case for studying NH multiband braiding and knot structures in four-band systems, which could offer insights for topological photonics and analog information processing applications.

关键词: exceptional point, knot structures, phase transitions, non-Abelian braids

Abstract: The strong connection between braids and knots provides valuable insights into studying the topological state and phase classification of various physical systems. The phenomenon of non-Hermitian (NH) two- and three-band braiding has received widespread attention. However, a systematic exploration and visualization of non-Abelian braiding and the associated knot transformations in four-band systems remains unexplored. Here, we propose a theoretical model of NH four-band braiding, provide its phase diagram, and establish its trivial, Abelian, and non-Abelian braiding rules. Additionally, we report on special knots, such as the Hopf and Solomon links in braided knots, and reveal that their transformations are accompanied by and mediated through exceptional points. Our work provides a detailed case for studying NH multiband braiding and knot structures in four-band systems, which could offer insights for topological photonics and analog information processing applications.

Key words: exceptional point, knot structures, phase transitions, non-Abelian braids

中图分类号:  (Group theory)

  • 02.20.-a
03.65.Vf (Phases: geometric; dynamic or topological) 68.35.Rh (Phase transitions and critical phenomena)