TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.20.1.001
TI  - Hopf exceptional points
PY  - 2026/01/07
UR  - https://scipost.org/SciPostPhys.20.1.001
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 20
IS  - 1
SP  - 001
A1  - Yoshida, Tsuneya
AU  - Bergholtz, Emil
AU  - Bzdušek, Tomáš
AB  - 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},
}