2026/07/22 by Carl A. Kukkonen
#cond-mat.supr-con #cond-mat.str-el
paper · pdf · doi:10.5281/zenodo.21497366
The static local field factors of the uniform electron gas are known accurately from quantum Monte Carlo (QMC) calculations, but two of their most striking features have lacked a mechanism: G+ grows almost exactly as q2 up to nearly 2kF, and the violent 2kF physics of the Fermi surface leaves only a faint trace in it. Combining the textbook first-order local-field relation with the exact static exchange polarizability gives a compact exact benchmark: the universal exchange-only local field factor Gx(q,0) = -I(Q)Q2/L(Q)2, Q = q/2kF, with exact values (1/4)(q/kF)2 at small q, π2/6 at 2kF -- apparently never before stated as a local-field value -- and 1/3 at large q, giving the exchange-only spin-averaged contact value g(0) = 1/2 of the unpolarized gas (BDL 1977). Gx rises to a finite maximum of 1.9924 at 1.9685kF and passes through π2/6 at exactly 2kF with a slope diverging as ln3|q-2kF|. Against this benchmark, the 1980 BDL tabulation is accurate to about one percent below 1.5kF, while the 2024 McLachlan-variational kernel of Nazarov and Silkin is two-percent accurate only below 0.5kF, is a factor of 1.74 low at 2kF, and its large-q limit is inconsistent with the contact constraint. A spin-resolved decomposition of QMC local field factors about the exact baseline shows that, within the resolution and smoothness assumptions of the QMC-based representations, both features follow from a strong exchange-correlation cancellation: at the QMC point closest to 2kF (q = 2.01kF, rs = 2), correlation cancels 0.43(7) of the exact exchange value 1.33. Computed consistently at each wavevector, the static exchange-kernel thresholds derived from the closed form reproduce, to 0.2%, the finite-wavevector charge threshold rs ≈ 10.6 near q = 1.94kF obtained numerically in 1980, and recovered again in 2014.