(50% Seminar) Dielectric formalism of the 3D/2D uniform electron gas at finite temperatures

Warm dense matter (WDM) concerns partially ionized high energy density matter at near-solid mass densities and at temperatures exceeding 10000K. WDM lies at the intersection of condensed matter physics, plasma physics and dense liquid physics. It naturally occurs in dense astrophysical objects (giant gas planet interiors, brown dwarfs, neutron star crusts) and emerges on the path to inertial confinement fusion. Central to WDM research is the accurate description of the uniform electron gas (UEG) across dimensions and finite temperatures, a challenge due to the competing influences of Coulomb coupling, exchange, diffraction, and thermal effects.

Recent advances in experimental platforms, such as clean quantum wells and atomically thin materials, have enabled detailed studies of the two-dimensional electron gas (2DEG), highlighting the importance of finite-temperature effects even in highly controlled systems. While quantum Monte Carlo (QMC) remains the benchmark for accuracy, its computational expense limits full exploration of the phase diagram.

In this presentation, I will introduce modern computational methods for WDM and highlight recent developments in dielectric theory for both 2D and 3D systems. I will focus on advances in the self-consistent dielectric formalism, built on linear response theory, which incorporates exchange-correlation effects via local field factors and offers a tractable yet accurate approach in probing the WDM phase diagram.