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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.07344 |
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| _version_ | 1866912419112026112 |
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| author | Evangelista, Francesco A. |
| author_facet | Evangelista, Francesco A. |
| contents | Quantifying correlation and complexity in quantum many-body states is central to advancing theoretical and computational chemistry, physics, and quantum information science. This work introduces a novel framework, mutual correlation, based on the Frobenius norm squared of the two-body reduced density matrix cumulant. Through systematic partitioning of the cumulant norm, mutual correlation quantifies nonadditive correlations among interacting subsystems. Benchmark studies on model systems, including H$_{10}$, N$_{2}$, and p-benzyne, demonstrate its efficacy and computational advantage compared to entropy-based metrics such as orbital mutual information. Maximally correlated orbitals, obtained by maximizing a nonlinear cost function of the mutual correlation, are also considered to identify a basis-independent partitioning of correlation. This study suggests that mutual correlation is a broadly applicable metric, useful in active space selection and the interpretation of electronic states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07344 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mutual Correlation Evangelista, Francesco A. Chemical Physics Quantifying correlation and complexity in quantum many-body states is central to advancing theoretical and computational chemistry, physics, and quantum information science. This work introduces a novel framework, mutual correlation, based on the Frobenius norm squared of the two-body reduced density matrix cumulant. Through systematic partitioning of the cumulant norm, mutual correlation quantifies nonadditive correlations among interacting subsystems. Benchmark studies on model systems, including H$_{10}$, N$_{2}$, and p-benzyne, demonstrate its efficacy and computational advantage compared to entropy-based metrics such as orbital mutual information. Maximally correlated orbitals, obtained by maximizing a nonlinear cost function of the mutual correlation, are also considered to identify a basis-independent partitioning of correlation. This study suggests that mutual correlation is a broadly applicable metric, useful in active space selection and the interpretation of electronic states. |
| title | Mutual Correlation |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2506.07344 |