Wannier decay and the Thouless conjecture
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910927440314368 |
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| author | Becker, Simon Tao, Zhongkai Yang, Mengxuan |
| author_facet | Becker, Simon Tao, Zhongkai Yang, Mengxuan |
| contents | Non-trivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions which provide natural bases for spectral subspaces. For non-trivial Bloch bundles, we obtain decay rates of Wannier functions in dimensions $d=2,3$. For $d=2$, we construct Wannier functions with full asymptotics and optimal decay rate $\mathcal{O}(|x|^{-2})$ as conjectured by Thouless; for $d=3$, we construct Wannier functions with the uniform decay rate $\mathcal{O}(|x|^{-7/3})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wannier decay and the Thouless conjecture Becker, Simon Tao, Zhongkai Yang, Mengxuan Mathematical Physics Mesoscale and Nanoscale Physics Materials Science Spectral Theory Non-trivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions which provide natural bases for spectral subspaces. For non-trivial Bloch bundles, we obtain decay rates of Wannier functions in dimensions $d=2,3$. For $d=2$, we construct Wannier functions with full asymptotics and optimal decay rate $\mathcal{O}(|x|^{-2})$ as conjectured by Thouless; for $d=3$, we construct Wannier functions with the uniform decay rate $\mathcal{O}(|x|^{-7/3})$. |
| title | Wannier decay and the Thouless conjecture |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Materials Science Spectral Theory |
| url | https://arxiv.org/abs/2505.01999 |