Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems

Defective spectral degeneracy, known as exceptional point (EP), lies at the heart of various intriguing phenomena in optics, acoustics, and other nonconservative systems. Despite extensive studies in the past two decades, the collective behaviors (e.g., annihilation, coalescence, braiding, etc.) involving multiple exceptional points or lines and their interplay have been rarely understood. Here we put forward a universal non-Abelian conservation rule governing these collective behaviors in generic multiband non-Hermitian systems and uncover several counterintuitive phenomena. We demonstrate that two EPs with opposite charges (even the pairwise created) do not necessarily annihilate, depending on how they approach each other. Furthermore, we unveil that the conservation rule imposes strict constraints on the permissible exceptional-line configurations. It excludes structures like Hopf link yet permits novel staggered rings composed of noncommutative exceptional lines. These intriguing phenomena are illustrated by concrete models which could be readily implemented in platforms like coupled acoustic cavities, optical waveguides, and ring resonators. Our findings lay the cornerstone for a comprehensive understanding of the exceptional non-Abelian topology and shed light on the versatile manipulations and applications based on exceptional degeneracies in nonconservative systems.

Automated summary

Extensive studies have revealed a universal non-Abelian conservation rule governing the collective behaviors of multiple exceptional points or lines in generic multiband non-Hermitian systems. Surprisingly, two EPs with opposite charges may not annihilate, depending on their approach. Additionally, the conservation rule imposes constraints on the permissible exceptional-line configurations, allowing for structures such as staggered rings composed of noncommutative exceptional lines. These findings provide insights into the exceptional non-Abelian topology and offer possibilities for manipulating and utilizing exceptional degeneracies in nonconservative systems.