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

TL;DR

This paper develops new analytic continuation methods to derive the dynamic structure factor of the electron liquid from PIMC data across various temperatures, aiding experimental interpretation and theoretical modeling.

Contribution

It introduces a combined approach using maximum entropy and Gaussian kernel methods for analytic continuation of PIMC data, implemented in the PyLIT package.

Findings

Comparison of maximum entropy and Gaussian kernel methods reveals their respective advantages.

Results provide detailed $S(q, \, \omega)$ data for the electron liquid at different temperatures.

Potential applications include improved interpretation of x-ray scattering and exchange-correlation kernel development.

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.