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U(1)xSU(2) gauge invariance made simple for density functional approximations

机译：U（1）xSU（2）规范不变性使密度泛函近似变得简单

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摘要

A semirelativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach for noncollinear magnetism, spintronics, orbitronics, and topological states. The basic variables of this theory include the paramagnetic current and the spin-current density, besides the particle and the spin density, and the corresponding exchange-correlation (xc) energy functional is invariant under local U(l) x SU(2) gauge transformations. The xc-energy functional must be approximated to enable practical applications, but, contrary to the case of the standard density functional theory, finding simple approximations suited to deal with realistic atomistic inhomogeneities has been a long-standing challenge. Here we propose a way out of this impasse by showing that approximate gauge-invariant functionals can be easily generated from existing approximate functionals of ordinary density-functional theory by applying a simple minimal substitution on the kinetic energy density, which controls the short-range behavior of the exchange hole. Our proposal opens the way to the construction of approximate, yet nonempirical functionals, which do not assume weak inhomogeneity and therefore may have a wide range of applicability in atomic, molecular, and condensed matter physics.
机译：半相对论的密度泛函理论包括自旋轨道耦合和与电磁势相等的塞曼场，是一个吸引人的框架，可为非共线磁性，自旋电子学，双电子学和拓扑状态开发统一的第一性原理计算方法。该理论的基本变量除了粒子和自旋密度外，还包括顺磁电流和自旋电流密度，并且在局部U（l）x SU（2）规范下，相应的交换相关（xc）能量函数不变转变。必须对xc-能量泛函进行近似才能实现实际应用，但是与标准密度泛函理论的情况相反，找到适合于处理现实原子不均匀性的简单近似是一项长期的挑战。在这里，我们提出了一种解决这种僵局的方法，方法是通过对动能密度进行简单的最小替换，从而可以从普通密度泛函理论的现有近似泛函中轻松生成近似规范不变泛函。交换孔。我们的建议为构造近似但非经验的泛函开辟了道路，这些泛函不假定弱的不均匀性，因此在原子，分子和凝聚态物理中可能具有广泛的适用性。

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  • 来源
    《Physical review》 |2017年第3期|035141.1-035141.8|共8页
  • 作者

    S. Pittalis; G. Vignale; F. G. Eich;

  • 作者单位

    Istituto Nanoscienze, Consiglio Nazionale delle Ricerche, Via Campi 213A, 1-41125 Modena, Italy;

    Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA;

    Max Planck Institute for the Structure and Dynamics of Matter, Lumper Chaussee 149, D-22761 Hamburg, Germany;

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