Microscopic derivation of density functional theory for superfluid systems based on effective action formalism

TL;DR

This paper develops a microscopic density functional theory for superfluid systems using the effective action formalism within the functional renormalization group, deriving exact expressions for the Kohn-Sham potential including pairing effects.

Contribution

It introduces a novel formalism that derives the Kohn-Sham potential for superfluids from microscopic principles, incorporating pairing and external interactions systematically.

Findings

Derives the flow equation for the effective action from non-interacting to interacting systems.

Provides an exact expression for the Kohn-Sham potential including pairing.

Shows the formalism reproduces Hartree-Fock-Bogoliubov ground-state energy when correlations are neglected.

Abstract

Density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and nonlocal pairing densities and demonstrate that the Hohenberg-Kohn theorem for superfluid systems is established in terms of the effective action. The flow equation for the effective action is then derived, where the flow parameter runs from $0$ to $1$, corresponding to the non-interacting and interacting systems. From the flow equation and the variational equation that the equilibrium density satisfies, we obtain the exact expression for the Kohn-Sham potential generalized to including the pairing potentials. The resultant Kohn-Sham potential has a nice feature that it expresses the microscopic formulae of the external, Hartree, pairing, and exchange-correlation terms, separately. It is shown that our Kohn-Sham potential gives the ground-state energy of the Hartree-Fock-Bogoliubov theory by neglecting the correlations. An advantage of our exact formalism lies in the fact that it provides ways to systematically improve the correlation part.