Exact density-functional theory as parallel ensemble variational hierarchies: from Lieb's formulation to Kohn-Sham theory
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913073173889024 |
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| author | Sheng, Nan |
| author_facet | Sheng, Nan |
| contents | Exact density-functional theory is reconstructed here from its convex variational structure as two parallel exact ensemble hierarchies: an interacting hierarchy rooted in Lieb's ensemble formulation and a noninteracting hierarchy rooted in the exact noninteracting ensemble theory. The Kohn-Sham construction links the two on a common admissible density class. In this organization, Levy-Lieb, Hohenberg-Kohn, and ordinary determinant-based Kohn-Sham formulations appear as constrained specializations of broader ensemble variational structures. Fractional particle number and fractional occupations enter naturally in the same ensemble variational setting, while piecewise linearity, one-sided chemical potentials, derivative discontinuity, and Janak-type relations emerge as consequences of the associated variational geometry. We also clarify several distinctions that are often compressed together in standard expositions, including functional domain versus representability class, state-space realization versus density-level supporting-potential structure, and density reproduction versus spectral interpretation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23399 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact density-functional theory as parallel ensemble variational hierarchies: from Lieb's formulation to Kohn-Sham theory Sheng, Nan Chemical Physics Mathematical Physics Exact density-functional theory is reconstructed here from its convex variational structure as two parallel exact ensemble hierarchies: an interacting hierarchy rooted in Lieb's ensemble formulation and a noninteracting hierarchy rooted in the exact noninteracting ensemble theory. The Kohn-Sham construction links the two on a common admissible density class. In this organization, Levy-Lieb, Hohenberg-Kohn, and ordinary determinant-based Kohn-Sham formulations appear as constrained specializations of broader ensemble variational structures. Fractional particle number and fractional occupations enter naturally in the same ensemble variational setting, while piecewise linearity, one-sided chemical potentials, derivative discontinuity, and Janak-type relations emerge as consequences of the associated variational geometry. We also clarify several distinctions that are often compressed together in standard expositions, including functional domain versus representability class, state-space realization versus density-level supporting-potential structure, and density reproduction versus spectral interpretation. |
| title | Exact density-functional theory as parallel ensemble variational hierarchies: from Lieb's formulation to Kohn-Sham theory |
| topic | Chemical Physics Mathematical Physics |
| url | https://arxiv.org/abs/2603.23399 |