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Light-Matter Correlation Energy Functional of the Cavity-Coupled Two-Dimensional Electron Gas via Quantum Monte Carlo Simulations

Lukas Weber1,2, Miguel A. Morales1, Johannes Flick1,3,4, Shiwei Zhang1, and Angel Rubio2,1

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Phys. Rev. Lett. 135, 126901 – Published 17 September, 2025

DOI: https://doi.org/10.1103/lq1y-q74h

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 parametrization of the light-matter correlation energy as a functional of the cavity parameters and the electronic density. These results provide a crucial step toward 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.

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Phys. Rev. Lett. 135, 126901– Published 17 September, 2025
  • Received 9 January 2025
  • Revised 20 May 2025
  • Accepted 28 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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