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Dielectric formalism of the two-dimensional uniform electron gas at finite temperatures

Fotios Kalkavouras1, Tobias Dornheim2,3, Paul Hamann2,4, and Panagiotis Tolias1,*

  • *Contact author: tolias@kth.se
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Phys. Rev. B 114, 165111 – Published 8 September, 2026

DOI: https://doi.org/10.1103/rcgt-jdcr

Abstract

We present a comprehensive analysis of the two-dimensional uniform electron gas (2D-UEG, or more commonly 2DEG) at finite temperature, spanning a broad range of densities/coupling strengths (0.01≤rs≤20) and temperatures/degeneracy parameters (0.01≤Θ=kBT/EF≤10). Within the self-consistent dielectric formalism, we construct 2D versions of the Singwi-Tosi-Land-Sjölander (STLS) and hypernetted-chain (HNC) approximation–based schemes. We benchmark the accuracy of the STLS and the HNC schemes against new state-of-the-art path-integral Monte Carlo data. We also report structural and thermodynamic properties across the full (rs,Θ) phase diagram domain studied, identify regimes in which these schemes remain quantitatively reliable, and provide an accurate parametrization of the exchange-correlation free energy of the finite-temperature 2DEG.

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Phys. Rev. B 114, 165111– Published 8 September, 2026
  • Received 23 January 2026
  • Revised 29 May 2026
  • Accepted 24 August 2026
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