Effective Static Approximation: A Fast and Reliable Tool for Warm-Dense Matter Theory

We present an effective static approximation (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor S(q,ω), the static structure factor S(q), and the interaction energy v. The ESA combines the recent neural-net representation by T. Dornheim et al., [J. Chem. Phys. 151, 194104 (2019)] of the temperature-dependent LFC in the exact static limit with a consistent large wave-number limit obtained from quantum Monte Carlo data of the on-top pair distribution function g(0). It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by reevaluating the results of the recent x-ray Thomson scattering experiment on aluminum by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)]. We find that an accurate incorporation of electronic correlations in terms of the ESA leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.