A Universal Chern Model on Arbitrary Triangulations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917317072388096 |
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| author | Higson, Nigel Prodan, Emil |
| author_facet | Higson, Nigel Prodan, Emil |
| contents | Given a triangulation of a closed orientable surface, we place single-mode resonators or single-orbital artificial atoms at its vertices, edges and facets, and we devise near-neighbor hopping terms derived from the boundary and Poincaré duality maps of the simplicial complex of the triangulation. Regardless of the surface or its triangulation, these terms always lead to tight-binding Hamiltonians with large and clean topological spectral gaps, carrying non-trivial Chern numbers in the limit of infinite refinement of the triangulation. We confirm this via numerical simulations, and demonstrate how these models enable topological edge modes at the surfaces of real-world objects. Furthermore, we describe a metamaterial whose dynamics reproduces that of the proposed model, thus bringing the topological metamaterials closer to real-world applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20862 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Universal Chern Model on Arbitrary Triangulations Higson, Nigel Prodan, Emil Strongly Correlated Electrons Materials Science Mathematical Physics Operator Algebras Given a triangulation of a closed orientable surface, we place single-mode resonators or single-orbital artificial atoms at its vertices, edges and facets, and we devise near-neighbor hopping terms derived from the boundary and Poincaré duality maps of the simplicial complex of the triangulation. Regardless of the surface or its triangulation, these terms always lead to tight-binding Hamiltonians with large and clean topological spectral gaps, carrying non-trivial Chern numbers in the limit of infinite refinement of the triangulation. We confirm this via numerical simulations, and demonstrate how these models enable topological edge modes at the surfaces of real-world objects. Furthermore, we describe a metamaterial whose dynamics reproduces that of the proposed model, thus bringing the topological metamaterials closer to real-world applications. |
| title | A Universal Chern Model on Arbitrary Triangulations |
| topic | Strongly Correlated Electrons Materials Science Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2510.20862 |