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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.17245 |
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| _version_ | 1866916914202148864 |
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| author | Ferretti, Andrea Marzari, Nicola |
| author_facet | Ferretti, Andrea Marzari, Nicola |
| contents | We address the problem of interacting electrons in an external potential by introducing the occupied spectral density $ρ(\mathbf{r},ω)$ as fundamental variable. First, we formulate the problem using an embedding framework, and prove a one-to-one correspondence between a $ρ(\mathbf{r},ω)$ and the local dynamical external potential $v_{\text{ext}}(\mathbf{r},ω)$ that embeds the interacting electrons into an open quantum system. Then, we use the Klein functional to ($i$) define a universal functional of $ρ(\mathbf{r},ω)$, ($ii$) introduce a variational principle for the total energy as a functional of $ρ(\mathbf{r},ω)$, and ($iii$) formulate a non-interacting mapping of spectral self-consistent equations suitable for numerical applications. At variance with time-dependent density-functional theory, this formulation aims at studying charged excitations and electronic spectra -- including electronic correlations -- with a functional theory; An explicit and formally correct description of all electronic levels could also lead to more accurate approximations for the total energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional theory of the occupied spectral density Ferretti, Andrea Marzari, Nicola Materials Science We address the problem of interacting electrons in an external potential by introducing the occupied spectral density $ρ(\mathbf{r},ω)$ as fundamental variable. First, we formulate the problem using an embedding framework, and prove a one-to-one correspondence between a $ρ(\mathbf{r},ω)$ and the local dynamical external potential $v_{\text{ext}}(\mathbf{r},ω)$ that embeds the interacting electrons into an open quantum system. Then, we use the Klein functional to ($i$) define a universal functional of $ρ(\mathbf{r},ω)$, ($ii$) introduce a variational principle for the total energy as a functional of $ρ(\mathbf{r},ω)$, and ($iii$) formulate a non-interacting mapping of spectral self-consistent equations suitable for numerical applications. At variance with time-dependent density-functional theory, this formulation aims at studying charged excitations and electronic spectra -- including electronic correlations -- with a functional theory; An explicit and formally correct description of all electronic levels could also lead to more accurate approximations for the total energy. |
| title | Functional theory of the occupied spectral density |
| topic | Materials Science |
| url | https://arxiv.org/abs/2508.17245 |