# Functional-renormalization-group aided density-functional analysis for the correlation energy of the two-dimensional homogeneous electron gas

## TL;DR

This paper applies the functional-renormalization-group aided density-functional theory (FRG-DFT) to the 2D homogeneous electron gas, accurately capturing the correlation energy at high densities and showing promise for complex quantum systems.

## Contribution

First application of FRG-DFT to a multi-dimensional model, demonstrating its effectiveness in calculating correlation energies in the 2D electron gas.

## Key findings

- Reproduces exact high-density limit behavior.
- Shows good agreement with Monte Carlo results at high densities.
- Indicates larger discrepancies at lower densities.

## Abstract

The functional-renormalization-group aided density-functional theory (FRG-DFT) is applied to the two-dimensional homogeneous electron gas (2DHEG). The correlation energy of the 2DHEG is derived as a function of the Wigner-Seitz radius $ r_{\rm s} $ directly. We find that our correlation energy completely reproduces the exact behavior at the high-density limit. For finite density, the result of FRG-DFT shows good agreement with the Monte Carlo (MC) results in the high-density region, although the discrepancy between FRG-DFT and MC results becomes larger as the system becomes more dilute. Our study is the first example in which the FRG-DFT is applied to more-than-one-dimensional models, and shows that the FRG-DFT is a feasible and promising method even for the analysis of realistic models for quantum many-body systems.