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

Abstract

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 \texttt{PyLIT} package [Benedix Robles \textit{et al.}, \textit{Comp.~Phys.~Comm.}~\textbf{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.