Nested Feature Spectrum Topology: Tripartite Topological Equivalence of Feature, Entanglement, and Wilson Loop Spectrum
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| Format: | Preprint |
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2026
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| _version_ | 1866917537278590976 |
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| author | Hung, Yi-Chun Ong, T. Tzen Lin, Hsin |
| author_facet | Hung, Yi-Chun Ong, T. Tzen Lin, Hsin |
| contents | Topological phases of matter are traditionally characterized through symmetry-based classifications. In cases of symmetry breaking, the projected spectrum - obtained by projecting the ground state onto the eigenstates of a pertinent quantum observable, such as spin or orbital angular momentum - provides a clear method for classifying topological phases. This approach underpins well-known frameworks such as spin-resolved topology and feature spectrum topology. Here we introduce nested feature spectrum topology, in which projection operators are applied recursively to subsectors of the feature spectrum, generating a hierarchy of feature spectra. We uncover a fundamental tripartite equivalence among the topology of feature, the entanglement, and the Wilson loop spectra in non-interacting fermionic systems. This equivalence reveals that the feature spectrum encodes the entanglement between sectors of the quantum observable, such as the spin-up and spin-down states in spin-resolved topology. We further prove that spectral flow in the entanglement spectrum and the Wilson loop winding in the feature spectrum are equivalent manifestations of the feature-energy complementarity: the appearance of gapless spectral flow in either energy or projected spectra on the boundary. This complementarity refines the conventional bulk-boundary correspondence by demonstrating that topological boundary modes may persist in the feature spectrum even when energy spectra are gapped. Our results provide a deeper understanding and solid foundation for the origin of band topology in the feature spectrum. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13128 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nested Feature Spectrum Topology: Tripartite Topological Equivalence of Feature, Entanglement, and Wilson Loop Spectrum Hung, Yi-Chun Ong, T. Tzen Lin, Hsin Mesoscale and Nanoscale Physics Materials Science Quantum Physics Topological phases of matter are traditionally characterized through symmetry-based classifications. In cases of symmetry breaking, the projected spectrum - obtained by projecting the ground state onto the eigenstates of a pertinent quantum observable, such as spin or orbital angular momentum - provides a clear method for classifying topological phases. This approach underpins well-known frameworks such as spin-resolved topology and feature spectrum topology. Here we introduce nested feature spectrum topology, in which projection operators are applied recursively to subsectors of the feature spectrum, generating a hierarchy of feature spectra. We uncover a fundamental tripartite equivalence among the topology of feature, the entanglement, and the Wilson loop spectra in non-interacting fermionic systems. This equivalence reveals that the feature spectrum encodes the entanglement between sectors of the quantum observable, such as the spin-up and spin-down states in spin-resolved topology. We further prove that spectral flow in the entanglement spectrum and the Wilson loop winding in the feature spectrum are equivalent manifestations of the feature-energy complementarity: the appearance of gapless spectral flow in either energy or projected spectra on the boundary. This complementarity refines the conventional bulk-boundary correspondence by demonstrating that topological boundary modes may persist in the feature spectrum even when energy spectra are gapped. Our results provide a deeper understanding and solid foundation for the origin of band topology in the feature spectrum. |
| title | Nested Feature Spectrum Topology: Tripartite Topological Equivalence of Feature, Entanglement, and Wilson Loop Spectrum |
| topic | Mesoscale and Nanoscale Physics Materials Science Quantum Physics |
| url | https://arxiv.org/abs/2603.13128 |