Overhauser's spin-density wave in exact-exchange spin density functional theory

TL;DR

This paper investigates the spin density wave state in the uniform electron gas within exact-exchange noncollinear spin DFT, revealing conditions for instability and the nature of self-consistent solutions, including excited-state determinants.

Contribution

It demonstrates that the SDW instability in exact-exchange spin-DFT occurs only below a critical density and explores the nature of self-consistent solutions involving excited-state Slater determinants.

Findings

SDW instability occurs only below a critical density in exact-exchange spin-DFT.

Non-self-consistent SDW solutions can have lower energy than paramagnetic states.

Self-consistent solutions can involve excited-state Slater determinants with partial band occupation.

Abstract

The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in Hartree-Fock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin density wave for all densities, in exact-exchange spin-DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a non-interacting SDW ground state Slater determinant with energy lower than the corresponding paramagnetic state, this Slater determinant is not a self-consistent solution of the Optimized Effective Potential (OEP) integral equations of noncollinear spin-DFT. A selfconsistent solution of the OEP equations which gives an even lower energy can be found using an excited-state Slater determinant where only orbitals with single-particle energies in the lower of two bands are occupied while orbitals in the second band remain unoccupied even if their energies are below the Fermi energy.