Hopf exceptional points, by Tsuneya Yoshida, Emil J. Bergholtz, Tomáš Bzdušek

SciPost Physics Home Authoring Refereeing Submit a manuscript About Hopf exceptional points Tsuneya Yoshida, Emil J. Bergholtz, Tomáš Bzdušek SciPost Phys. 20, 001 (2026) · published 7 January 2026 doi: 10.21468/SciPostPhys.20.1.001 pdf BiBTeX RIS Submissions/Reports 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 \enquote{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. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.1.001TI - Hopf exceptional pointsPY - 2026/01/07UR - https://scipost.org/SciPostPhys.20.1.001JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 1SP - 001A1 - Yoshida, TsuneyaAU - Bergholtz, Emil J.AU - Bzdušek, TomášAB - 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 \enquote{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.ER - × @Article{10.21468/SciPostPhys.20.1.001, title={{Hopf exceptional points}}, author={Tsuneya Yoshida and Emil J. Bergholtz and Tomáš Bzdušek}, journal={SciPost Phys.}, volume={20}, pages={001}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.1.001}, url={https://scipost.org/10.21468/SciPostPhys.20.1.001},} Ontology / Topics See full Ontology or Topics database. Topological semimetals Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 Tsuneya Yoshida, 3 Emil J. Bergholtz, 4 Tomáš Bzdušek 1 Eidgenössische Technische Hochschule Zürich / Swiss Federal Institute of Technology in Zurich (ETH) [ETH Zurich] 2 京都大学 / Kyoto University 3 Stockholm University [Univ Stockholm] 4 Universität Zürich / University of Zurich [UZH] Funders for the research work leading to this publication Göran Gustafssons Stiftelser 日本学術振興会 / Japan Society for the Promotion of Science [JSPS] Knut och Alice Wallenbergs Stiftelse / Knut and Alice Wallenberg Foundation Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung / Swiss National Science Foundation [SNF] Yamada Science Foundation