Local field corrections to the retarded cumulant Green's function

Local field corrections (LFC) to the screened coulomb potential beyond the RPA have been found to be important in calculations of exchange and correlation properties, particularly at low densities r_s=10 and highter. Typically these corrections are included by adding a static momentum dependent Hubbard correction G(q) to the density response function Χ = Χ₀ + Χ₀ K Χ, where K(q) = v_q (1-G(q)) = v_q + f_xc(q), Χ₀(q,ω) is the Lindhard function, and f_xc is the TDDFT kernel. The local field factor G(q) = q² K_xc(q)/4π is parabolic in q at small q and constant near unity at large q, reflecting the crossover from screened to unscreened behavior of the dielectric response with increasing q. We have tested several approximations for G(q) including a simple interpolation formula G(q) =aq²/(1+b q²) with b ~ a = K_xc(0)/4π. Here we report calculations of exchange-correlation properties obtained using the retarded cumulant Green’s function [Phys. Rev. B 90, 085112 (2014), Phys. Rev. B 100, 195144 (2019)] and G₀W appraoches with the LFC dielectric function replacing the RPA and compared with accurate quantum Monte Carlo (QMC) results. [Phys. Rep. 744, 1 (2018)]. Although improved accuracy compared with QMC is obtained for the LFC corrected RC approach at r_s=10, the agreement becomes significantly worse at r_s =20.