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

Warm dense matter is of high current interest for many applications, including astrophysics and fusion research. Yet, the accurate description of electronic correlation effects at these conditions is most difficult, and often computationally intensive ab-initio methods have to be used. Here we present the effective static approximation (ESA) [1] to the local field correction (LFC) of the electron gas, which 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 with no computational extra cost compared to the random phase approximation (RPA).

More specifically, the ESA combines the recent neural-net representation of ab-initio path integral Monte Carlo results [2] of the temperature-dependent LFC in the exact static limit with a consistent large wave-number limit. It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by re-evaluating the recent x-ray Thomson scattering experiment on aluminum by Sperling et al. [3]. We find that an accurate incorporation of electronic correlations within the ESA leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like 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, or for the computation of material properties like the thermal/electrical conductivity, stopping power, etc.

Finally, the ESA is now readily available as an analytical representation [4] and can be easily incorporated into existing codes.

[1] T. Dornheim et al., Phys. Rev. Lett. 125, 235001 (2020)

[2] T. Dornheim et al., J. Chem. Phys. 151, 194104 (2019)

[3] P. Sperling et al., Phys. Rev. Lett. 115, 115001 (2015)

[4] T. Dornheim et al., Phys. Rev. B 103, 165102 (2021)