Revisiting density-functional theory of the total current density

Abstract

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.

References in corpus (4)

• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• Non-existence of a Hohenberg-Kohn Variational Principle in Total Current Density Functional Theory
• Degenerate ground states and nonunique potentials: breakdown and restoration of density functionals
• Density-functional theory for internal magnetic fields

Cited by in corpus (2)

• The structure of the density-potential mapping. Part II: Including magnetic fields
• Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model