From Divergent Series to Geometry: Resurgence of the Quantum Metric
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917050048315392 |
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| author | Hernández, Marcos J. Díaz, Bogar Vergara, J. David |
| author_facet | Hernández, Marcos J. Díaz, Bogar Vergara, J. David |
| contents | In this work, we analyze perturbative expansions of the quantum metric tensor (QMT) in anharmonic oscillators, focusing on quartic, sextic, and $d$-dimensional models. Using high-order perturbation theory, we show that the divergent QMT series exhibit factorial growth. Our analysis identifies universal non-perturbative scales, with coefficients displaying large-order behavior consistent with resurgence theory. Then, we apply resurgence and Borel--Padé resummation to the QMT. Comparisons with exact diagonalization confirm that Borel--Padé resummations yield accurate results, especially for the ground state. For completeness, we also present the analysis of the energy eigenvalues in the examples. Our findings extend resurgent techniques from energies to the QMT, highlighting the interplay between quantum geometry and non-perturbative physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Divergent Series to Geometry: Resurgence of the Quantum Metric Hernández, Marcos J. Díaz, Bogar Vergara, J. David Quantum Physics Other Condensed Matter High Energy Physics - Theory In this work, we analyze perturbative expansions of the quantum metric tensor (QMT) in anharmonic oscillators, focusing on quartic, sextic, and $d$-dimensional models. Using high-order perturbation theory, we show that the divergent QMT series exhibit factorial growth. Our analysis identifies universal non-perturbative scales, with coefficients displaying large-order behavior consistent with resurgence theory. Then, we apply resurgence and Borel--Padé resummation to the QMT. Comparisons with exact diagonalization confirm that Borel--Padé resummations yield accurate results, especially for the ground state. For completeness, we also present the analysis of the energy eigenvalues in the examples. Our findings extend resurgent techniques from energies to the QMT, highlighting the interplay between quantum geometry and non-perturbative physics. |
| title | From Divergent Series to Geometry: Resurgence of the Quantum Metric |
| topic | Quantum Physics Other Condensed Matter High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.25907 |