Hopf Exceptional Points

• URL: http://arxiv.org/abs/2504.13012v2
• Date: Thu, 01 May 2025 00:12:22 GMT
• Title: Hopf Exceptional Points
• Authors: Tsuneya Yoshida, Emil J. Bergholtz, Tomáš Bzdušek,
• Abstract summary: We introduce a class of Hopf exceptional points that are protected by the Hopf invariants.<n>Based on higher homotopy groups of spheres, we predict the existence of multifold HEPs and symmetry-protected HEPs with non-Hermitian topology.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanical metamaterials to open quantum systems. Here, we introduce a class of Hopf exceptional points (HEPs) that are protected by the Hopf invariants (including the higher-dimensional generalizations) and which exhibit phenomenology sharply distinct from conventional exceptional points. Saliently, owing to their $\mathbb{Z}_2$ topological invariant related to the Witten anomaly, three-fold HEPs and symmetry-protected five-fold HEPs act as their own ``antiparticles". Furthermore, based on higher homotopy groups of spheres, we predict the existence of multifold HEPs and symmetry-protected HEPs with non-Hermitian topology captured by a range of finite groups (such as $\mathbb{Z}_3$, $\mathbb{Z}_{12}$, or $\mathbb{Z}_{24}$) beyond the periodic table of Bernard-LeClair symmetry classes.

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