Revisiting density-functional theory of the total current density
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| Format: | Preprint |
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2020
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| _version_ | 1866914979164192768 |
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| author | Laestadius, Andre Penz, Markus Tellgren, Erik I. |
| author_facet | Laestadius, Andre Penz, Markus Tellgren, Erik I. |
| contents | Density-functional theory requires an extra variable besides the electron density in order to properly incorporate magnetic-field effects. In a time-dependent setting, the gauge-invariant, total current density takes that role. A peculiar feature of the static ground-state setting is, however, that the gauge-dependent paramagnetic current density appears as the additional variable instead. An alternative, exact reformulation in terms of the total current density has long been sought but to date a work by Diener is the only available candidate. In that work, an unorthodox variational principle was used to establish a ground-state density-functional theory of the total current density as well as an accompanying Hohenberg-Kohn-like result. We here reinterpret and clarify Diener's formulation based on a maximin variational principle. Using simple facts about convexity implied by the resulting variational expressions, we prove that Diener's formulation is unfortunately not capable of reproducing the correct ground-state energy and, furthermore, that the suggested construction of a Hohenberg-Kohn map contains an irreparable mistake. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_12661 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Revisiting density-functional theory of the total current density Laestadius, Andre Penz, Markus Tellgren, Erik I. Chemical Physics Materials Science Density-functional theory requires an extra variable besides the electron density in order to properly incorporate magnetic-field effects. In a time-dependent setting, the gauge-invariant, total current density takes that role. A peculiar feature of the static ground-state setting is, however, that the gauge-dependent paramagnetic current density appears as the additional variable instead. An alternative, exact reformulation in terms of the total current density has long been sought but to date a work by Diener is the only available candidate. In that work, an unorthodox variational principle was used to establish a ground-state density-functional theory of the total current density as well as an accompanying Hohenberg-Kohn-like result. We here reinterpret and clarify Diener's formulation based on a maximin variational principle. Using simple facts about convexity implied by the resulting variational expressions, we prove that Diener's formulation is unfortunately not capable of reproducing the correct ground-state energy and, furthermore, that the suggested construction of a Hohenberg-Kohn map contains an irreparable mistake. |
| title | Revisiting density-functional theory of the total current density |
| topic | Chemical Physics Materials Science |
| url | https://arxiv.org/abs/2012.12661 |