Exchange kernel $f^h_x(q,ω)$ of electron liquid from the variational principle of McLachlan
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912046978695168 |
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| author | Nazarov, Vladimir U. Silkin, Vyacheslav M. |
| author_facet | Nazarov, Vladimir U. Silkin, Vyacheslav M. |
| contents | By minimizing, in the $L_2$ norm, the difference between the left- and the right-hand sides of the time-dependent Schrödinger equation, the variational principle of McLachlan (McLVP) [A. McLachlan, Molecular Physics {\bf 8}, 39 (1964)] provides a powerful tool for the generation of equations of motion. If the trial wave function is the Slater determinant, McLVP produces a temporally and spatially nonlocal exchange potential [V. U. Nazarov, Phys. Rev. B {\bf 87}, 165125 (2013)]. We study the performance of the corresponding wave-vector and frequency-dependent exchange kernel $f^h_x(q,ω)$ of the homogeneous electron liquid. While the McLVP-based $f^h_x(q,ω)$ lacks correlations by construction, we find that it accurately accounts for exchange, reproducing features in the quantum Monte Carlo data, which the known constraint-based kernels miss. We argue that the complementary use of the McLVP- and the constraint-based exchange-correlation kernels will enhance the performance of the linear response time-dependent density functional theory of the electron liquid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16294 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exchange kernel $f^h_x(q,ω)$ of electron liquid from the variational principle of McLachlan Nazarov, Vladimir U. Silkin, Vyacheslav M. Strongly Correlated Electrons Chemical Physics By minimizing, in the $L_2$ norm, the difference between the left- and the right-hand sides of the time-dependent Schrödinger equation, the variational principle of McLachlan (McLVP) [A. McLachlan, Molecular Physics {\bf 8}, 39 (1964)] provides a powerful tool for the generation of equations of motion. If the trial wave function is the Slater determinant, McLVP produces a temporally and spatially nonlocal exchange potential [V. U. Nazarov, Phys. Rev. B {\bf 87}, 165125 (2013)]. We study the performance of the corresponding wave-vector and frequency-dependent exchange kernel $f^h_x(q,ω)$ of the homogeneous electron liquid. While the McLVP-based $f^h_x(q,ω)$ lacks correlations by construction, we find that it accurately accounts for exchange, reproducing features in the quantum Monte Carlo data, which the known constraint-based kernels miss. We argue that the complementary use of the McLVP- and the constraint-based exchange-correlation kernels will enhance the performance of the linear response time-dependent density functional theory of the electron liquid. |
| title | Exchange kernel $f^h_x(q,ω)$ of electron liquid from the variational principle of McLachlan |
| topic | Strongly Correlated Electrons Chemical Physics |
| url | https://arxiv.org/abs/2408.16294 |