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arXiv · 2008.05919

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

Takeru Yokota·Haruki Kasuya·Kenichi Yoshida·Teiji Kunihiro
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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.

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Takeru Yokota, Haruki Kasuya, Kenichi Yoshida, Teiji Kunihiro. 2020-08-20. Microscopic derivation of density functional theory for superfluid systems based on effective action formalism. https://doi.org/10.1093/ptep%2Fptaa173

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