Temperature dependence of the dynamic structure factor of the electron liquid via analytic continuation

We present new analytic continuation results for the dynamic structure factor $S(\mathbf{q},\omega )$ of the uniform electron liquid based on quasi-exact \emph{ab initio} path integral Monte Carlo (PIMC) data for the imaginary-time density–density correlation function $F(\mathbf{q},\tau )$ across a broad range of temperatures. For this purpose, we employ both a traditional maximum entropy method solver, and a pre-optimized sparse Gaussian kernel representation as it has been implemented in the recent $\mathtt{\text{PyLIT}}$ package [Benedix Robles $\mathit{\text{et}}\mathit{\text{al.}}$, $\mathit{\text{Comp.}}\mathit{\text{Phys.}}\mathit{\text{Comm.}}$~$\mathbf{\text{319}}$, 109904 (2026)], and we identify potential advantages and disadvantages in both. We expect our results to be interesting for a broad range of topics, including the interpretation of x-ray Thomson scattering experiments with extreme states of matter and the construction of improved exchange–correlation kernels for linear-response time-dependent density functional theory.