Energy response and spatial alignment of the perturbed electron gas

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the harmonically perturbed uniform electron gas (UEG) for different densities and temperatures. This allows us to study the linear response of the UEG with respect to different contributions to the total energy for different wave numbers. We find that the induced change in the interaction energy exhibits a non-monotonic behaviour, and becomes negative for intermediate wave numbers. This effect is strongly dependent on the coupling strength and can be traced back to the spatial alignment of electrons introduced in earlier works [T.~Dornheim \emph{et al.}, Communications Physics \textbf{5}, 304 (2022)]. The observed quadratic dependence on the perturbation amplitude in the limit of weak perturbations and the quartic dependence of the perturbation amplitude corrections are consistent with linear and non-linear versions of the density stifness theorem. All PIMC simulation results are freely available online and can be used to benchmark new methods, or as input for other calculations.