Failure of the local density approximation in time-dependent spin density functional theory

TL;DR

This paper reveals a fundamental nonlocality issue in time-dependent spin density functional theory's exchange-correlation potentials, and proposes using spin current density as a solution to achieve local expressions.

Contribution

The paper identifies a severe nonlocality problem in TD-SDFT and introduces a local formulation based on spin currents to address it.

Findings

Nonlocality in exchange-correlation potentials is more severe in TD-SDFT.

Using spin current density as a basic variable provides a local expression for exchange-correlation fields.

The proposed approach offers a new way to improve TD-SDFT calculations.

Abstract

It has been known for some time that the exchange-correlation potential in time-dependent density functional theory is an intrinsically nonlocal functional of the density as soon as one goes beyond the adiabatic approximation. In this paper we show that a much more severe nonlocality problem, with a completely different physical origin, plagues the exchange-correlation potentials in time-dependent spin density functional theory. We show how the use of the spin current density as the basic variable solves this problem, and we provide an explicit local expression for the exchange-correlation fields as functionals of the spin currents.