Ab initio path integral Monte Carlo simulation of the uniform electron gas in the high energy density regime

The response of the uniform electron gas (UEG) to an external perturbation is of paramount importance for many applications. Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [\textit{J.~Chem.~Phys.}~\textbf{151}, 194104 (2019)] and strongly coupled electron liquid [\textit{Phys.~Rev.~B}~\textbf{101}, 045129 (2020)] conditions based on exact \textit{ab initio} path integral Monte Carlo (PIMC) simulations. In the present work, we further complete our current description of the UEG by exploring the high energy density regime, which is relevant for, e.g., astrophysical applications and inertial confinement fusion experiments. To this end, we present extensive new PIMC results for the static density response in the range of $0.05 \leq r_s \leq 0.5$ and $0.85\leq\theta\leq8$. These data are subsequently used to benchmark the accuracy of the widely used random phase approximation and the dielectric theory by Singwi, Tosi, Land, and Sj\"olander (STLS). Moreover, we compare our results to configuration PIMC data where they are available and find perfect agreement with a relative accuracy of $0.001-0.01\%$. All PIMC data are available online.