Revisiting density-functional theory of the total current density

Fuente: arXiv
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Main Authors: Laestadius, Andre, Penz, Markus, Tellgren, Erik I.
Format: Preprint
Published: 2020
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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
id 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