Exact and approximate relations for the spin-dependence of the exchange energy in high magnetic fields

TL;DR

This paper derives exact and approximate relations for the spin-dependent exchange energy in high magnetic fields within density-functional theory, connecting polarized and unpolarized limits to generalize spin scaling relations.

Contribution

It introduces a method to reconstruct the exchange energy functional from extreme spin polarization limits, extending spin-DFT to current-DFT and high magnetic fields.

Findings

Reconstruction of exchange energy from unpolarized and fully polarized limits.

Generalization of Oliver-Perdew spin scaling relations to current-DFT.

Derivation of high-field local-spin-density approximation for current-DFT.

Abstract

The exchange energy of an arbitrary collinear-spin many-body system in an external magnetic field is a functional of the spin-resolved charge and current densities, $E_x[n_{\uparrow},n_{\downarrow},j_{\uparrow},j_{\downarrow}]$. Within the framework of density-functional theory (DFT), we show that the dependence of this functional on the four densities can be fully reconstructed from either of two extreme limits: a fully polarized system or a completely unpolarized system. Reconstruction from the limit of an unpolarized system yields a generalization of the Oliver-Perdew spin scaling relations from spin-DFT to current-DFT. Reconstruction from the limit of a fully polarized system is used to derive the high-field form of the local-spin-density approximation to current-DFT and to magnetic-field DFT.