Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914685321740288 |
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| author | Goshen, Yuli Kraisler, Eli |
| author_facet | Goshen, Yuli Kraisler, Eli |
| contents | Description of many-electron systems with a fractional electron number $N_\textrm{tot}$ and fractional spin $M_\textrm{tot}$ is of great importance in physical chemistry, solid state physics and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system, and characterize the dependence of the energy and the spin-densities on both $N_\textrm{tot}$ and $M_\textrm{tot}$, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at constant $N_\textrm{tot}$, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03465 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized Goshen, Yuli Kraisler, Eli Materials Science Atomic Physics Chemical Physics Computational Physics Description of many-electron systems with a fractional electron number $N_\textrm{tot}$ and fractional spin $M_\textrm{tot}$ is of great importance in physical chemistry, solid state physics and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system, and characterize the dependence of the energy and the spin-densities on both $N_\textrm{tot}$ and $M_\textrm{tot}$, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at constant $N_\textrm{tot}$, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods. |
| title | Energy of a many-electron system in an ensemble ground-state, versus electron number and spin: piecewise-linearity and flat plane condition generalized |
| topic | Materials Science Atomic Physics Chemical Physics Computational Physics |
| url | https://arxiv.org/abs/2308.03465 |