Ab initio construction of the energy density functional for electron systems with the functional-renormalization-group-aided density functional theory

TL;DR

This paper presents an  initio method using the functional renormalization group to construct an energy density functional for electron systems, accurately capturing correlation energies without fitting, and demonstrating its effectiveness in atomic calculations.

Contribution

It introduces a novel  initio approach to construct the energy density functional using the functional renormalization group, avoiding empirical fitting.

Findings

Reproduces exact high-density correlation energies for the electron gas.

Agrees well with Monte Carlo data across various densities.

Provides comparable results to conventional LDA in atomic calculations.

Abstract

We show an $\textit{ab initio}$ construction of the energy density functional (EDF) for electron systems using the functional renormalization group. The correlation energies of the homogeneous electron gas given in our framework reproduce the exact behavior at high density and agree with the Monte-Carlo data in a wide range of densities. Our analytic technique enables us to get the correlation energies efficiently for various densities, which realizes the determination of EDF in the local density approximation (LDA) without any fitting for physically relevant densities. Applied to the Kohn-Sham calculation for the noble gas atoms, our EDF shows comparable results to those of other conventional ones in LDA.