Exceptional point-induced knot structure transformations in 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.