Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Thomas Chuna, Maximilian P. Böhme, Tobias Dornheim

Abstract

We present new analytic continuation results for the dynamic structure factor $S(\mathbf{q},ω)$ 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 $F(\mathbf{q},τ)$ 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.

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 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 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.

Paper Structure

This paper contains 7 sections, 15 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theory
  3. Path integral Monte Carlo
  4. Linear response theory
  5. Analytic continuation
  6. Results
  7. Discussion and Outlook

Figures (3)

  • Figure 1: Ab initio PIMC results for the ITCF $F(\mathbf{q},\tau)$ of the UEG with $N=34$ at $r_s=20$ for $\Theta=0.75$ (left) and $\Theta=2$ (right).
  • Figure 2: Heatmaps: analytic continuation results for the dynamic structure factor of the UEG with $N=34$ at $r_s=20$ for different values of the reduced temperature $\Theta$; frequencies are given in units of the plasma frequency $\omega_\textnormal{p}=\sqrt{3/r_s^3}$ and wavenumbers in units of the Fermi wavenumber $q_\textnormal{F}=(9\pi/4)^{1/3}/r_s$. The top and bottom rows have been obtained using PyLIT and the standard MEM. We note that the color scale changes between plots. The top and bottom cyan curves show the position of the maximum of $S(\mathbf{q},\omega)$ computed within RPA and static approximation [i.e., $G(\mathbf{q},\omega)\equiv0$ and $G(\mathbf{q},\omega)\equiv G(\mathbf{q},0)$ in Eq. (\ref{['eq:define_G']})], and the black curves show the same information for the analytic continuation.
  • Figure 3: ITCF $F(\mathbf{q},\tau)$ for selected wavenumbers $q$ at $\Theta=0.75$ (left), $\Theta=2$ (middle) and $\Theta=8$ (right). The red symbols correspond to the results for typical formulation with Bryan's MEM algorithm, the results for kernel formulation with PyLIT code are green, and the static approximation is depicted in blue. The insets show the absolute deviation from the PIMC ground truth with the same color code.