Towards full instanton trans-series in Hofstadter's butterfly
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913507587391488 |
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| author | Gu, Jie Xu, Zhaojie |
| author_facet | Gu, Jie Xu, Zhaojie |
| contents | The trans-series completion of perturbative series of a wide class of quantum mechanical systems can be determined by combining the resurgence program and extra input coming from exact WKB analysis. In this paper, we reexamine the Harper-Hofstadter model and its spectrum, Hofstadter's butterfly, in light of recent developments. We demonstrate the connection between the perturbative energy series of the Harper-Hofstadter model and the vev of $1/2$-BPS Wilson loop of 5d SYM and clarify the differences between their non-perturbative corrections. Taking insights from the cosine potential model, we construct the full energy trans-series for flux $ϕ=2π/Q$ and provide numerical evidence with remarkably high precision. Finally, we revisit the problem of self-similarity of the butterfly and discuss the possibility of a completed version of the Rammal-Wilkinson formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards full instanton trans-series in Hofstadter's butterfly Gu, Jie Xu, Zhaojie High Energy Physics - Theory Mesoscale and Nanoscale Physics Mathematical Physics The trans-series completion of perturbative series of a wide class of quantum mechanical systems can be determined by combining the resurgence program and extra input coming from exact WKB analysis. In this paper, we reexamine the Harper-Hofstadter model and its spectrum, Hofstadter's butterfly, in light of recent developments. We demonstrate the connection between the perturbative energy series of the Harper-Hofstadter model and the vev of $1/2$-BPS Wilson loop of 5d SYM and clarify the differences between their non-perturbative corrections. Taking insights from the cosine potential model, we construct the full energy trans-series for flux $ϕ=2π/Q$ and provide numerical evidence with remarkably high precision. Finally, we revisit the problem of self-similarity of the butterfly and discuss the possibility of a completed version of the Rammal-Wilkinson formula. |
| title | Towards full instanton trans-series in Hofstadter's butterfly |
| topic | High Energy Physics - Theory Mesoscale and Nanoscale Physics Mathematical Physics |
| url | https://arxiv.org/abs/2406.18098 |