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 ...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.62575099,62075059,61405058)Guangdong Basic and Applied Basic Research Foundation(Grant No.2024A1515011353)+2 种基金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)Scientific Research Foundation of Hunan Provincial Education Department(Grant No.21A0013)。
文摘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.
