Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems

TL;DR

This paper reveals a universal non-Abelian conservation rule governing collective behaviors of multiple exceptional points in multiband non-Hermitian systems, uncovering counterintuitive phenomena and topological constraints.

Contribution

It introduces a novel non-Abelian conservation law for exceptional points, explaining complex collective behaviors and topological configurations in non-Hermitian multiband systems.

Findings

Two EPs with opposite charges may not annihilate depending on their approach.

The conservation rule constrains exceptional-line configurations, excluding Hopf links.

Novel staggered rings of noncommutative exceptional lines are permitted.

Abstract

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 \textit{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.