(Spin-)density-functional theory for open-shell systems: exact magnetization density functional for the half-filled Hubbard trimer

Abstract

According to the Hohenberg-Kohn theorem of density-functional theory (DFT), all observable quantities of systems of interacting electrons can be expressed as functionals of the ground-state density. This includes, in principle, the spin polarization (magnetization) of open-shell systems; the explicit form of the magnetization as a functional of the total density is, however, unknown. In practice, open-shell systems are always treated with spin-DFT, where the basic variables are the spin densities. Here, the relation between DFT and spin-DFT for open-shell systems is illustrated and the exact magnetization density functional is obtained for the half-filled Hubbard trimer. Errors arising from spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are analyzed and partially cured via the exact magnetization functional.

arXiv comment10 pages, 7 figures

References in corpus (16)

• Finding Density Functionals with Machine Learning
• Understanding and reducing errors in density functional calculations
• Spin in Density-Functional Theory
• Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid
• Quantifying Density Errors in DFT
• The Hubbard Dimer: A density functional case study of a many-body problem
• Spin electric effects in molecular antiferromagnets
• What can Mott insulators teach us about density-functional theory (and vice versa)?
• First-principle studies of the spin-orbit and the Dzyaloshinskii-Moriya interactions in the \{Cu${}_3$\} single-molecule magnet
• Landscape of an exact energy functional
• Linear response time-dependent density functional theory of the Hubbard dimer
• Simple parametrization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
• Density-functional theory for systems with noncollinear spin: orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
• The many-electron ground-state determines uniquely the potential in Spin-Density-Functional Theory for non-collinear magnetism
• Melting a Hubbard dimer: benchmarks of `ALDA' for quantum thermodynamics
• Testing density-functional approximations on a lattice and the limits of the related Hohenberg-Kohn-type theorem

Cited by in corpus (5)

• Interaction-resistant metals in multicomponent Fermi systems
• Benchmark for Ab Initio Prediction of Magnetic Structures based on Cluster-Multipole Theory
• Exchange-correlation magnetic fields in spin-density-functional theory
• Magnetization dynamics with time-dependent spin-density functional theory: significance of exchange-correlation torques
• Geometrical Perspective on Spin-Lattice Density-Functional Theory