Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems

Area of Science:

• Physics
• Quantum Mechanics
• Non-Hermitian Systems

Background:

• Exceptional points (EPs) are critical degeneracies in nonconservative systems, crucial for optics and acoustics.
• Understanding collective behaviors of multiple EPs, such as annihilation and braiding, remains a significant challenge.

Purpose of the Study:

• To introduce a universal non-Abelian conservation rule for multiband non-Hermitian systems.
• To explore novel phenomena arising from the interplay of multiple EPs and exceptional lines.

Main Methods:

• Development of a universal non-Abelian conservation rule.
• Theoretical analysis of collective behaviors of EPs in generic multiband non-Hermitian systems.
• Illustration with concrete models in coupled acoustic cavities and optical waveguides.

Main Results:

• Demonstration that pairwise created EPs with opposite charges do not always annihilate.
• Unveiling strict constraints on exceptional-line configurations, excluding Hopf links but permitting staggered rings.
• Identification of novel collective behaviors and counterintuitive phenomena governed by the non-Abelian rule.

Conclusions:

• The non-Abelian conservation rule provides a foundational understanding of exceptional non-Abelian topology.
• Findings enable versatile manipulations and applications of exceptional degeneracies in nonconservative systems.
• The study opens new avenues for exploring complex behaviors in engineered physical systems.