重新审视总电流密度的密度泛函理论
Revisiting density-functional theory of the total current density
AI总结：
本文重新审视Diener提出的基于总电流密度的基态密度泛函理论，利用极大极小变分原理证明其无法重现正确基态能量，且其Hohenberg-Kohn映射构造存在不可修复的错误。
摘要：
密度泛函理论除了电子密度之外还需要一个额外变量，以便恰当地纳入磁场效应。在含时情形下，规范不变的总电流密度承担了这一角色。然而，静态基态情形的一个特殊之处在于，规范相关的顺磁电流密度反而作为额外变量出现。长期以来，人们一直在寻求用总电流密度表述的另一种精确重构，但迄今为止，Diener的一项工作仍是唯一可用的候选方案。在该工作中，使用了一种非正统的变分原理来建立总电流密度的基态密度泛函理论，并给出了一个伴随的类Hohenberg-Kohn结果。我们在此基于极大极小变分原理重新解释并澄清Diener的表述。利用所得变分表达式所蕴含的关于凸性的简单事实，我们证明Diener的表述不幸无法重现正确的基态能量，并且进一步证明其所建议的Hohenberg-Kohn映射构造包含一个不可修复的错误。
英文摘要：
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.
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