The light-matter correlation energy functional of the cavity-coupled two-dimensional electron gas via quantum Monte Carlo simulations

TL;DR

This paper develops a quantum Monte Carlo method to accurately simulate cavity-coupled two-dimensional electron gases, providing a new functional for light-matter interactions that enhances the predictive power of quantum materials modeling.

Contribution

It introduces a QED auxiliary-field quantum Monte Carlo method and a parameterization of the light-matter correlation energy functional for cavity-coupled systems.

Findings

Modified weak-coupling perturbation theory is highly accurate.

Finite-size effects can be significantly reduced.

Provides a numerical foundation for QED density functional theory.

Abstract

We perform extensive simulations of the two-dimensional cavity-coupled electron gas in a modulating potential as a minimal model for cavity quantum materials. These simulations are enabled by a newly developed quantum-electrodynamical (QED) auxiliary-field quantum Monte Carlo method. We present a procedure to greatly reduce finite-size effects in such calculations. Based on our results, we show that a modified version of weak-coupling perturbation theory is remarkably accurate for a large parameter region. We further provide a simple parameterization of the light-matter correlation energy as a functional of the cavity parameters and the electronic density. These results provide a numerical foundation for the development of the QED density functional theory, which was previously reliant on analytical approximations, to allow quantitative modeling of a wide range of systems with light-matter coupling.