The Density Functional via Effective Action

TL;DR

This paper provides a rigorous derivation of the density functional in Hohenberg-Kohn theory using the effective action approach, enabling a loop expansion of the exchange-correlation functional in terms of Kohn-Sham orbitals.

Contribution

It introduces an auxiliary field method that allows the exchange-correlation functional to be expressed solely with Kohn-Sham orbitals, regardless of the electric coupling strength.

Findings

Loop expansion reorganized in terms of Kohn-Sham orbitals

Derivation applicable without small electric coupling constant

Provides a rigorous theoretical foundation for density functional methods

Abstract

A rigorous derivation of the density functional via the effective action in the Hohenberg-Kohn theory is outlined. Using the auxiliary field method, in which the electric coupling constant $e^2$ need not be small, we show that the loop expansion of the exchange-correlation functional can be reorganized so as to be expressed entirely in terms of the Kohn-Sham single-particle orbitals and energies.