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.