Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain
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arXiv
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| Format: | Preprint |
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2024
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| author | Vladaj, Matthieu Marécat, Quentin Senjean, Bruno Saubanère, Matthieu |
| author_facet | Vladaj, Matthieu Marécat, Quentin Senjean, Bruno Saubanère, Matthieu |
| contents | The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges such as the lack of Kohn--Sham scheme and the complexity of the pure $N$-representability conditions are still impeding its wild utilization. Fortunately, ensemble $N$-representability conditions derived in the natural orbital basis are known and trivial, such that almost every functionals of the 1-RDM are actually natural orbital functionals which do not perform well for all the correlation regimes. In this work, we propose a variational minimization scheme in the ensemble $N$-representable domain that is not restricted to the natural orbital representation of the 1-RDM. We show that splitting the minimization into the diagonal and off-diagonal part of the 1-RDM can open the way toward the development of functionals of the orbital occupations, which remains a challenge for the generalization of site-occupation functional theory in chemistry. Our approach is tested on the uniform Hubbard model using the Müller and the Töws--Pastor functionals, as well as on the dihydrogen molecule using the Müller functional. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_10593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain Vladaj, Matthieu Marécat, Quentin Senjean, Bruno Saubanère, Matthieu Quantum Physics Strongly Correlated Electrons The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges such as the lack of Kohn--Sham scheme and the complexity of the pure $N$-representability conditions are still impeding its wild utilization. Fortunately, ensemble $N$-representability conditions derived in the natural orbital basis are known and trivial, such that almost every functionals of the 1-RDM are actually natural orbital functionals which do not perform well for all the correlation regimes. In this work, we propose a variational minimization scheme in the ensemble $N$-representable domain that is not restricted to the natural orbital representation of the 1-RDM. We show that splitting the minimization into the diagonal and off-diagonal part of the 1-RDM can open the way toward the development of functionals of the orbital occupations, which remains a challenge for the generalization of site-occupation functional theory in chemistry. Our approach is tested on the uniform Hubbard model using the Müller and the Töws--Pastor functionals, as well as on the dihydrogen molecule using the Müller functional. |
| title | Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2405.10593 |