First-Principles Effective Mass in the Three-Dimensional Uniform Electron Gas
Phys. Rev. Lett. 137, 206501 – Published 9 November, 2026
DOI: https://doi.org/10.1103/b8qp-v38m
Abstract
The quasiparticle effective mass of the three-dimensional uniform electron gas is a fundamental Fermi-liquid parameter whose value and density dependence have remained controversial for decades. Using renormalized perturbation theory with explicit counterterms, we determine in the metallic regime () from first principles by two complementary routes—the self-energy and the forward-scattering four-point vertex via the -wave spin-symmetric Landau parameter —that agree within uncertainties at each density through the sixth renormalized order. The resulting remains close to unity throughout the metallic regime, with a shallow nonmonotonic density dependence—a minimum near followed by a gentle upturn—reflecting the interplay of exchange and dynamical screening in the self-energy, and disfavoring strong monotonic suppression. This near-unity behavior is traced to the structural dominance of long-range charge fluctuations, whose isotropy in angular-momentum space suppresses that controls .