Exceptional rings and non-Abelian topology in non-Hermitian high-spin systems

Topological phases featuring non-Abelian charges have garnered significant attention in recent years. In parallel, the study of multiband exceptional topology in non-Hermitian systems has emerged as a prominent research direction. In this study, we investigate a parity–time (PT) symmetric Hamiltonian, which hosts both conventional non-Abelian topological phases (NATPs) and hybrid phases. We propose an experimental scheme using spin-1 atoms with spin–orbit coupling trapped in two-dimensional (2D) lattices. Before adding a non-Hermitian term, we find the emergence of distinct topological phases mixed by two NATPs and establish their connection with NATPs theory. When a non-Hermitian term that preserves PT symmetry protection was introduced, stable second-order exceptional rings and third-order exceptional points emerge and they drive the edge states to manifest as discontinuous Fermi arcs in the surface Brillouin zone. However, with the variation of the non-Hermitian term, it is rather intriguing that two types of exceptional rings here transition from being internally tangent to externally tangent, transforming into a new topological phase equivalent to the Hermitian case. This research provides deeper insights into the nature of NATPs and the topological implications of exceptional structures, contributing to the field of topological physics.