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

TL;DR

This paper introduces a novel approach combining the functional renormalization group with the Kohn-Sham scheme to improve the derivation of energy density functionals, demonstrating rapid convergence in a zero-dimensional benchmark.

Contribution

The authors develop a new method that integrates the functional renormalization group with density functional theory, providing a practical way to quantify uncertainties and achieve fast convergence.

Findings

Fast convergence to exact results in zero-dimensional $\

demonstrates effectiveness even in strong coupling regimes,

provides a practical uncertainty quantification method.

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 $\varphi^4$ 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.