First-Principles Effective Mass in the Three-Dimensional Uniform Electron Gas

TL;DR

This study accurately determines the quasiparticle effective mass in the three-dimensional uniform electron gas using first-principles methods, revealing it remains close to the electron mass with a subtle density dependence.

Contribution

First-principles calculation of the effective mass in the 3D UEG using two complementary methods, resolving longstanding controversies.

Findings

Effective mass remains near unity across the metallic regime.

Density dependence shows a shallow minimum near r_s≈1.

Results disfavor strong monotonic suppression of the effective mass.

Abstract

The quasiparticle effective mass $m^*$ of the three-dimensional uniform electron gas (UEG) 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 $m^*$ in the metallic regime ($r_s \le 6$) from first principles by two complementary routes -- the self-energy and the forward-scattering four-point vertex via the $p$-wave spin-symmetric Landau parameter $F_1^s$ -- that agree within uncertainties at each density through sixth renormalized order. The resulting $m^*/m$ remains close to unity throughout the metallic regime, with a shallow non-monotonic density dependence -- a minimum near $r_s\approx 1$ followed by a gentle upturn -- reflecting the interplay of exchange and dynamical screening in the self-energy, and disfavoring strong monotonic suppression. This finding supports a physical picture for the metallic UEG in which dominant charge correlations are concentrated in nearly forward scattering and generate only a weak $F_1^s$ component.