Synthetic Non-Abelian Gauge Fields for Non-Hermitian Systems
Open accessAbstract
Non-Abelian gauge fields are versatile tools for synthesizing topological phenomena, but have so far been mostly studied in Hermitian systems, where gauge flux has to be defined from a closed loop in order for vector potentials, whether Abelian or non-Abelian, to become physically meaningful. We show that this condition can be relaxed in non-Hermitian systems by proposing and studying a generalized Hatano-Nelson model with imbalanced non-Abelian hopping. Despite lacking gauge flux in one dimension, non-Abelian gauge fields create rich non-Hermitian topological consequences. With SU(2) gauge fields, the braiding degrees that can be achieved are twice the highest hopping order of a lattice model, indicating the utility of spinful freedom to attain high-order nontrivial braiding. At both ends of an open chain, non-Abelian gauge fields lead to the simultaneous presence of non-Hermitian skin modes, whose population can be effectively tuned near the exceptional points. Generalizing to two dimensions, the gauge invariance of Wilson loops can also break down in non-Hermitian lattices dressed with non-Abelian gauge fields. Toward realization, we present a concrete experimental proposal for non-Abelian gauge fields in non-Hermitian systems via the synthetic frequency dimension of a polarization-multiplexed fiber ring resonator.
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The resonance locations in the time-dependent transmission spectra correspond to the band energies along the sampling line Lφ: ky = M kx + φ (mod 2π) in the two-dimensional Brillouin zone.
“the resonance locations in the time-dependent transmission spectra correspond to the band energies along the sampling line L φ : k y = M k x + φ (mod 2π) in the two-dimensional Brillouin zone.”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [55]
The paper’s discussion of its Bloch Hamiltonian and eigen-energies (Eq. 3–5; page unavailable) concerns a single momentum k. Searches for transmission spectra and the proposed sampling line found no passage connecting resonance locations to band energies along ky = M kx + φ in a two-dimensional Brillouin zone. (LLM, conf=0.75)
Experimental — accuracy not yet measuredIn a synthetic frequency lattice, δω is interpreted as the Floquet quasi-energy of the system, and t is interpreted as the wavevector k since time is the reciprocal quantity of frequency.
“In a synthetic frequency lattice, δω is interpreted as the Floquet quasi-energy of the system, and t is interpreted as the wavevector k since time is the reciprocal quantity of frequency [54,55].”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [55]
The passage on potential experimental platforms (indexed as Abstract; page unavailable) mentions a synthetic frequency dimension, while the Bloch-Hamiltonian passage uses k for the model’s bands. Neither identifies δω as Floquet quasi-energy or equates time with k. Searches for those terms and the time–frequency relationship found no passage addressing the claimed interpretation. (LLM, conf=0.72)
Experimental — accuracy not yet measured
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- Authors
- Pang, Z., Wong, B. T. T., Hu, J., & Yang, Y.
- Affiliations
- University of Hong Kong (HK)
- University of Shanghai for Science and Technology (CN)
- Corresponding author
- Yang, Yi
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2024-01-24
- Volume
- 132
- Issue
- 4
- Pages
- 043804-043804
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W4391165330
- Cited by
- 41
- References
- 79
- Citations by year
- 2026: 17 · 2025: 18 · 2024: 6
- FWCI
- 6.52
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion, cc-by)
- Figshare (submittedVersion, cc-by)
- The HKU Scholars Hub (University of Hong Kong) (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Funders
- University of Hong Kong (STG3/E-704/23-N)
- National Natural Science Foundation of China (HKU 12222417)
- Young Scientists Fund
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Keywords
- Yang-Mills fields, non-Hermitian systems, Hatano-Nelson model, exceptional points, Wilson loops, non-Abelian braiding, SU(2) gauge fields, non-Hermitian topology, fiber ring resonator, polarization multiplexing, synthetic dimensions, open chains
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