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

    Pengcheng Hou1,*,†, Daniel Cerkoney2,*, Zhiyi Li3,1,*, Tao Wang4, Xiansheng Cai5, Lei Wang4, Gabriel Kotliar2, Youjin Deng3,1,‡, and Kun Chen5,2,6,§

    • *These authors contributed equally to this work.
    • †Contact author: houpc@hfnl.cn
    • ‡Contact author: yjdeng@ustc.edu.cn
    • §Contact author: chenkun@itp.ac.cn

    Phys. Rev. Lett. 137, 206501 – Published 9 November, 2026

    DOI: https://doi.org/10.1103/b8qp-v38m

    Abstract

    The quasiparticle effective mass m* 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 m* in the metallic regime (rs≤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 F1s—that agree within uncertainties at each density through the sixth renormalized order. The resulting m*/m remains close to unity throughout the metallic regime, with a shallow nonmonotonic density dependence—a minimum near rs≈1 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 F1s that controls m*/m.

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