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Peer-reviewedCC BY 4.0Quantum

Evidence for Exceptional Points as Topological Defects

  • Chia-Yi Ju1,2,3,4
  • Szu-Ming Chen5
5 affiliations
  1. 1Department of Physics, National Sun Yat-sen University, Kaohsiung 804201, Taiwan
  2. 2Center for Theoretical and Computational Physics, National Sun Yat-sen University, Kaohsiung 804201, Taiwan
  3. 3Research Center for Quantum Computing and Quantum Materials, National Sun Yat-sen University, Kaohsiung 804201, Taiwan
  4. 4Physics Division, National Center for Theoretical Sciences, Taipei 106319, Taiwan
  5. 5National Science and Technology Museum, Kaohsiung 807044, Taiwan
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Abstract

Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the existing literature focuses on eigenstate subbundles, where geometric properties like Berry curvature arise, this work considers the entire Hilbert space bundle. Although the Hilbert space bundle has been found to be locally flat, suggesting that the system's topology may appear trivial, we revisit this assumption. Specifically, we examine how an arbitrary quantum state evolves when transported along closed parameter loops, a phenomenon characterized by holonomy. Our results demonstrate that nontrivial holonomy can emerge in the presence of exceptional points. Consequently, exceptional points naturally manifest as topological defects. Finally, we show that this nontrivial topology manifests in physical, time-dependent evolutions, providing a simple experimental signature to detect exceptional points by comparing state transport along distinct paths.

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Cite

BibTeXRIS
BibTeX
@article{ju2026evidence,
  title = {{Evidence for Exceptional Points as Topological Defects}},
  author = {Chia-Yi Ju and Szu-Ming Chen},
  journal = {Quantum},
  year = {2026},
  month = sep,
  doi = {10.22331/q-2026-09-30-2220},
  url = {https://quantum-journal.org/papers/q-2026-09-30-2220/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Evidence for Exceptional Points as Topological Defects
AU  - Chia-Yi Ju
AU  - Szu-Ming Chen
PY  - 2026
DA  - 2026/09/30
JO  - Quantum
DO  - 10.22331/q-2026-09-30-2220
UR  - https://quantum-journal.org/papers/q-2026-09-30-2220/
AB  - Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the existing literature focuses on eigenstate subbundles, where geometric properties like Berry curvature arise, this work considers the entire Hilbert space bundle. Although the Hilbert space bundle has been found to be locally flat, suggesting that the system's topology may appear trivial, we revisit this assumption. Specifically, we examine how an arbitrary quantum state evolves when transported along closed parameter loops, a phenomenon characterized by holonomy. Our results demonstrate that nontrivial holonomy can emerge in the presence of exceptional points. Consequently, exceptional points naturally manifest as topological defects. Finally, we show that this nontrivial topology manifests in physical, time-dependent evolutions, providing a simple experimental signature to detect exceptional points by comparing state transport along distinct paths.
SN  - 2521-327X
ER  -