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

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.

26 pages, 1 figure, v2: sentences added to abstract & introduction, symbols unified

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• Exact evolution equation for the effective potential
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction
• The Kinetic Energy Density in Kohn-Sham Density Functional Theory
• Effective Field Theory for Dilute Fermions with Pairing
• Towards Density Functional Calculations from Nuclear Forces

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