First-Principles Effective Mass in the Three-Dimensional Uniform Electron Gas
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 (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 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 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 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 F1s component.
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BibTeX
@misc{hou2026firstprinciples,
title = {{First-Principles Effective Mass in the Three-Dimensional Uniform Electron Gas}},
author = {Pengcheng Hou and Daniel Cerkoney and Zhiyi Li and Tao Wang and Xiansheng Cai and Lei Wang and Gabriel Kotliar and Youjin Deng and Kun Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.02294},
eprint = {2605.02294},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.02294},
}
RIS
TY - UNPB
TI - First-Principles Effective Mass in the Three-Dimensional Uniform Electron Gas
AU - Pengcheng Hou
AU - Daniel Cerkoney
AU - Zhiyi Li
AU - Tao Wang
AU - Xiansheng Cai
AU - Lei Wang
AU - Gabriel Kotliar
AU - Youjin Deng
AU - Kun Chen
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2605.02294
UR - https://arxiv.org/abs/2605.02294
AB - 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 ≤ 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≈ 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.
ER -