Topological Triviality of Flat Hamiltonians
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913848237228032 |
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| author | Sathe, Pratik Roy, Rahul |
| author_facet | Sathe, Pratik Roy, Rahul |
| contents | Landau levels play a key role in theoretical models of the quantum Hall effect. Each Landau level is degenerate, flat and topologically non-trivial. Motivated by Landau levels, we study tight-binding Hamiltonians whose energy levels are all flat. We demonstrate that in two dimensions, for such Hamiltonians, the flat bands must be topologically trivial. To that end, we show that the projector onto each flat band is necessarily strictly local. Our conclusions do not need the assumption of lattice translational invariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06487 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological Triviality of Flat Hamiltonians Sathe, Pratik Roy, Rahul Mesoscale and Nanoscale Physics Materials Science Strongly Correlated Electrons Mathematical Physics Landau levels play a key role in theoretical models of the quantum Hall effect. Each Landau level is degenerate, flat and topologically non-trivial. Motivated by Landau levels, we study tight-binding Hamiltonians whose energy levels are all flat. We demonstrate that in two dimensions, for such Hamiltonians, the flat bands must be topologically trivial. To that end, we show that the projector onto each flat band is necessarily strictly local. Our conclusions do not need the assumption of lattice translational invariance. |
| title | Topological Triviality of Flat Hamiltonians |
| topic | Mesoscale and Nanoscale Physics Materials Science Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2309.06487 |