Functional Renormalization Group and Kohn-Sham scheme in Density Functional Theory

Abstract

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the ${\phi }^4$ theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

6 pages, 3 figures, and 1 table

References in corpus (4)

• Exact evolution equation for the effective potential
• van der Waals forces in density functional theory: The vdW-DF method
• Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
• Two-particle irreducible functional renormalization group schemes---a comparative study

Cited by in corpus (24)

• Skyrme functional with tensor terms from \textit{ab initio} calculations of neutron-proton drops
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
• Emergent Hadrons and Diquarks
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• Functional renormalization-group calculation of the equation of state of one-dimensional nuclear matter inspired by the Hohenberg--Kohn theorem
• Toward ab initio charge symmetry breaking in nuclear energy density functionals
• Improvement of functionals in density functional theory by the inverse Kohn--Sham method and density functional perturbation theory
• Ab-initio description of excited states of a one-dimensional nuclear matter with the Hohenberg-Kohn-theorem-inspired functional-renormalization-group method
• Application of Coulomb energy density functional for atomic nuclei: Case studies of local density approximation and generalized gradient approximation
• Functional-renormalization-group aided density-functional analysis for the correlation energy of the two-dimensional homogeneous electron gas
• Ab initio construction of the energy density functional for electron systems with the functional-renormalization-group-aided density functional theory
• Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
• Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system
• 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
• Construction of energy density functional for arbitrary spin polarization using functional renormalization group
• Physics-informed neural networks for solving functional renormalization group on a lattice
• 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
• Thermal liquid-gas phase transition in a quasi-one-dimensional dipolar Fermi gas
• Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids
• Effects of Tensor Force in the Relativistic Scheme: A Case Study of Neutron Drops
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems