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

S. Pittalis, G. Vignale, and F. G. Eich
Phys. Rev. B 96, 035141 – Published 21 July 2017

Abstract

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(1)×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.

  • Received 23 April 2017

DOI:https://doi.org/10.1103/PhysRevB.96.035141

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Pittalis1,*, G. Vignale2, and F. G. Eich3

  • 1Istituto Nanoscienze, Consiglio Nazionale delle Ricerche, Via Campi 213A, I-41125 Modena, Italy
  • 2Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
  • 3Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany

  • *stefano.pittalis@nano.cnr.it

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Issue

Vol. 96, Iss. 3 — 15 July 2017

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