non-Abelian aspects of non-Hermitian bands

Abstract:

Defective spectral degeneracy, known as exceptional point (EP), lies at the heart of a variety of intriguing phenomena in optics, acoustics, cold atoms, and other non-conservative systems. Despite extensive studies in the past two decades, a holistic framework accounting for the collective behaviors (e.g., annihilation, coalescence, braiding, etc.) involving multiple exceptional points or lines and their interplay is still lacking. Here we formulate an exceptional band theory by exploiting based homotopy groups and put forward a universal non-Abelian conservation rule governing these collective phenomena in generic multiband non-Hermitian systems. Starting from this framework, we uncover several counter-intuitive 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 non-Abelian conservation rule imposes strict constraints on the permissible exceptional-line configurations. It excludes structures like Hopf link yet permits novel staggered rings composed of non-commutative exceptional lines. These intriguing phenomena are illustrated by concrete models and could be readily implemented in platforms like coupled acoustic cavities. 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 non-conservative systems.

Bio:

中国科学院物理研究所“百人特聘研究员”，博士生导师。2011年9月毕业于中国科学技术大学零零班。2016年7月在中国科学院物理研究所获得物理博士学位。2016年9月-2021年9月分别在德州大学达拉斯分校，匹兹堡大学和乔治梅森大学从事博士后研究。2021年9月加入中国科学院物理研究所。主要研究方向为拓扑凝聚态理论，量子动力学，原子分子与光物理和量子模拟理论。