Filling-Sensitive Spectral Complexity from Hilbert-Space Holonomy in Fragmented Non-Hermitian Systems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911698400575488 |
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| author | Wang, Jiong-Hao Zelenayova, Maria Ekman, Christopher Bergholtz, Emil J. |
| author_facet | Wang, Jiong-Hao Zelenayova, Maria Ekman, Christopher Bergholtz, Emil J. |
| contents | We show that Hilbert-space holonomy provides a geometric organizing principle for spectral reality in fragmented non-Hermitian many-body systems, complementary to conventional symmetry protection. In two minimal fragmented models, complex spectra can arise only within the most symmetric sectors: half filling in the fermion model and zero magnetization in the spin chain. Adding or removing a single particle, or flipping a single spin, renders the spectra entirely real despite unchanged periodic boundary conditions, reminiscent of boundary-condition sensitivity in systems with a non-Hermitian skin effect. We explain this by viewing nonreciprocal hopping amplitudes as a discrete gauge field on the Krylov graph: trivial holonomy permits a diagonal similarity transformation to the Hermitian limit, whereas nontrivial holonomy obstructs it and allows complex spectra. In certain regimes, trivial holonomy admits an emergent-boundary interpretation, and longer-range models exhibit finite real and complex regions governed by the same criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19740 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Filling-Sensitive Spectral Complexity from Hilbert-Space Holonomy in Fragmented Non-Hermitian Systems Wang, Jiong-Hao Zelenayova, Maria Ekman, Christopher Bergholtz, Emil J. Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics Optics Quantum Physics We show that Hilbert-space holonomy provides a geometric organizing principle for spectral reality in fragmented non-Hermitian many-body systems, complementary to conventional symmetry protection. In two minimal fragmented models, complex spectra can arise only within the most symmetric sectors: half filling in the fermion model and zero magnetization in the spin chain. Adding or removing a single particle, or flipping a single spin, renders the spectra entirely real despite unchanged periodic boundary conditions, reminiscent of boundary-condition sensitivity in systems with a non-Hermitian skin effect. We explain this by viewing nonreciprocal hopping amplitudes as a discrete gauge field on the Krylov graph: trivial holonomy permits a diagonal similarity transformation to the Hermitian limit, whereas nontrivial holonomy obstructs it and allows complex spectra. In certain regimes, trivial holonomy admits an emergent-boundary interpretation, and longer-range models exhibit finite real and complex regions governed by the same criterion. |
| title | Filling-Sensitive Spectral Complexity from Hilbert-Space Holonomy in Fragmented Non-Hermitian Systems |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics Optics Quantum Physics |
| url | https://arxiv.org/abs/2605.19740 |