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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.14028 |
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| _version_ | 1866913948748480512 |
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| author | Ji, Guangyue Palomino, David E. Goldman, Nathan Ozawa, Tomoki Riseborough, Peter Wang, Jie Mera, Bruno |
| author_facet | Ji, Guangyue Palomino, David E. Goldman, Nathan Ozawa, Tomoki Riseborough, Peter Wang, Jie Mera, Bruno |
| contents | Geometry plays a fundamental role in a wide range of physical responses, from anomalous transport coefficients to their related sum rules. Notable examples include the quantization of the Hall conductivity and the Souza-Wilkens-Martin (SWM) sum rule -- both valid at zero temperature, independent of interactions and disorder. The finite-temperature generalization of the SWM sum rule has been explored in the literature, revealing deep connections to the geometry of density matrices. Building on recent advances in time-dependent geometric frameworks, we propose a time-dependent quantum geometric tensor for thermal density matrices. This formalism provides a unified interpretation of known sum rules within the framework of the fluctuation-dissipation theorem, further elucidating their fundamental geometric origin. In addition, it provides experimentally accessible methods to probe quantum geometry beyond the zero-temperature regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density Matrix Geometry and Sum Rules Ji, Guangyue Palomino, David E. Goldman, Nathan Ozawa, Tomoki Riseborough, Peter Wang, Jie Mera, Bruno Mesoscale and Nanoscale Physics Geometry plays a fundamental role in a wide range of physical responses, from anomalous transport coefficients to their related sum rules. Notable examples include the quantization of the Hall conductivity and the Souza-Wilkens-Martin (SWM) sum rule -- both valid at zero temperature, independent of interactions and disorder. The finite-temperature generalization of the SWM sum rule has been explored in the literature, revealing deep connections to the geometry of density matrices. Building on recent advances in time-dependent geometric frameworks, we propose a time-dependent quantum geometric tensor for thermal density matrices. This formalism provides a unified interpretation of known sum rules within the framework of the fluctuation-dissipation theorem, further elucidating their fundamental geometric origin. In addition, it provides experimentally accessible methods to probe quantum geometry beyond the zero-temperature regime. |
| title | Density Matrix Geometry and Sum Rules |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2507.14028 |