Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -

TL;DR

This paper introduces a two-point particle irreducible renormalization group approach to density functional theory, providing a formalism that can potentially analyze ground-state properties of complex many-body systems from microscopic interactions.

Contribution

It develops a novel 2PPI RG formalism for DFT and demonstrates its application to toy models, bridging microscopic interactions and ground-state properties.

Findings

Formalism relates RG flow to density functional theory.

Application to toy models shows potential for studying nuclear systems.

Provides a detailed analysis of the RG flow equation structure.

Abstract

We discuss a two-point particle irreducible (2PPI) approach to many-body physics which relies on a renormalization group (RG) flow equation for the associated effective action. In particular, the general structure and properties of this RG flow equation are analyzed in detail. Moreover, we discuss how our 2PPI RG approach relates to Density Functional Theory and argue that it can in principle be used to study ground-state properties of non-relativistic many-body systems from microscopic interactions, such as (heavy) nuclei. For illustration purposes, we use our formalism to compute the ground-state properties of two toy models.