Refining ensemble $N$-representability of one-body density matrices from partial information
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911624234795008 |
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| author | Liebert, Julia Schouten, Anna O. Avdic, Irma Schilling, Christian Mazziotti, David A. |
| author_facet | Liebert, Julia Schouten, Anna O. Avdic, Irma Schilling, Christian Mazziotti, David A. |
| contents | The $N$-representability problem places fundamental constraints on reduced density matrices (RDMs) that originate from physical many-fermion quantum states. Motivated by recent developments in functional theories, we introduce a hierarchy of ensemble one-body $N$-representability problems that incorporate partial knowledge of the one-body reduced density matrices (1RDMs) within an ensemble of $N$-fermion states with fixed weights $w_i$. Specifically, we propose a systematic relaxation that reduces the refined problem -- where full 1RDMs are fixed for certain ensemble elements -- to a more tractable form involving only natural occupation number vectors. Remarkably, we show that this relaxed problem is related to a generalization of Horn's problem, enabling an explicit solution by combining its constraints with those of the weighted ensemble $N$-representability conditions. An additional convex relaxation yields a convex polytope that provides physically meaningful restrictions on lattice site occupations in ensemble density functional theory for excited states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refining ensemble $N$-representability of one-body density matrices from partial information Liebert, Julia Schouten, Anna O. Avdic, Irma Schilling, Christian Mazziotti, David A. Quantum Physics Chemical Physics The $N$-representability problem places fundamental constraints on reduced density matrices (RDMs) that originate from physical many-fermion quantum states. Motivated by recent developments in functional theories, we introduce a hierarchy of ensemble one-body $N$-representability problems that incorporate partial knowledge of the one-body reduced density matrices (1RDMs) within an ensemble of $N$-fermion states with fixed weights $w_i$. Specifically, we propose a systematic relaxation that reduces the refined problem -- where full 1RDMs are fixed for certain ensemble elements -- to a more tractable form involving only natural occupation number vectors. Remarkably, we show that this relaxed problem is related to a generalization of Horn's problem, enabling an explicit solution by combining its constraints with those of the weighted ensemble $N$-representability conditions. An additional convex relaxation yields a convex polytope that provides physically meaningful restrictions on lattice site occupations in ensemble density functional theory for excited states. |
| title | Refining ensemble $N$-representability of one-body density matrices from partial information |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2506.09960 |