The Kinetic Energy Density in Kohn-Sham Density Functional Theory

Abstract

This work continues a program to systematically generalize the Skyrme Hartree-Fock method for medium and heavy nuclei by applying effective field theory (EFT) methods to Kohn-Sham density functional theory (DFT). When conventional Kohn-Sham DFT for Coulomb systems is extended beyond the local density approximation, the kinetic energy density tau is sometimes included in energy functionals in addition to the fermion density. However, a local (semi-classical) expansion of tau is used to write the energy as a functional of the density alone, in contrast to the Skyrme approach. The difference is manifested in different single-particle equations, which in the Skyrme case include a spatially varying effective mass. Here we show how to generalize the EFT framework for DFT derived previously to reconcile these approaches. A dilute gas of fermions with short-range interactions confined by an external potential serves as a model system for comparisons and for testing power-counting estimates of new contributions to the energy functional.

27 pages, 8 figures, some corrections and clarifications

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Cited by in corpus (25)

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• Relativistic nuclear energy density functional constrained by low-energy QCD
• Density Matrix Expansion for Low-Momentum Interactions
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Large-Scale Self-Consistent Nuclear Mass Calculations
• Effective Field Theory and Finite Density Systems
• Density Functional Theory: Methods and Problems
• Density functional theory for fermions close to the unitary regime
• Effective Field Theory for Dilute Fermions with Pairing
• Eft for DFT
• Natural Units For Nuclear Energy Density Functional Theory
• Single-Particle Properties from Kohn-Sham Green's Functions
• Density-functional theory for the pairing Hamiltonian
• Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
• Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory
• Energy functional for the three-level Lipkin model
• Occupation number-based energy functional for nuclear masses
• KIDS density functional for deformed nuclei: Examples of the even-even Nd isotopes
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Nuclear kinetic density from ab initio theory
• Correlation Testing in Nuclear Density Functional Theory
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory