Dynamic exchange-correlation effects in the strongly coupled electron liquid

We present the first quasi-exact $\mathit{\text{ab}}\mathit{\text{initio}}$ path integral Monte Carlo (PIMC) results for the dynamic local field correction $\tilde{G}(\mathbf{q},z_l;r_s,\mathrm{\Theta })$ in the imaginary Matsubara frequency domain, focusing on the strongly coupled finite temperature uniform electron gas. These allow us to investigate the impact of dynamic exchange–correlation effects onto the static structure factor. Our results provide a straightforward explanation for previously reported spurious effects in the so-called $\mathit{\text{static}}\mathit{\text{approximation}}$ [Dornheim $\mathit{\text{et}}\mathit{\text{al.}}$, $\mathit{\text{Phys.}}\mathit{\text{Rev.}}\mathit{\text{Lett.}}$~$\mathbf{\text{125}}$, 235001 (2020)], where the frequency-dependence of the local field correction is neglected. Our findings hint at the intriguing possibility of constructing an analytical four-parameter representation of $\tilde{G}(\mathbf{q},z_l;r_s,\mathrm{\Theta })$ valid for a substantial part of the phase diagram, which would constitute key input for thermal density functional theory simulations.