Short wavelength limit of the dynamic Matsubara local field correction

TL;DR

This study uses ab initio PIMC simulations to analyze the short wavelength behavior of the dynamic Matsubara local field correction in the uniform electron gas, confirming theoretical limits and revealing complex convergence patterns.

Contribution

It provides the first extensive ab initio data on the dynamic local field correction at high wave numbers, confirming asymptotic limits and exploring behavior in warm dense matter and strongly coupled regimes.

Findings

Excellent agreement with analytical asymptotic limit for static local field correction.

Empirical confirmation that the short wavelength limit is independent of Matsubara frequency.

Complex non-monotonic convergence observed in strongly coupled regimes.

Abstract

We investigate the short wavelength limit of the dynamic Matsubara local field correction $\widetilde{G}(\mathbf{q},z_l)$ of the uniform electron gas based on direct \emph{ab initio} path integral Monte Carlo (PIMC) results over an unprecedented range of wavenumbers, $q\lesssim20q_\textnormal{F}$, where $q_\textnormal{F}$ is the Fermi wavenumber. We find excellent agreement with the analytically derived asymptotic limit by Hou \emph{et al.}~[\textit{Phys.~Rev.~B}~\textbf{106}, L081126 (2022)] for the static local field correction and empirically confirm the independence of the short wavelength limit with respect to the Matsubara frequency $z_l$. In the warm dense matter regime, we find that the onset of the quantum tail in the static local field correction closely coincides with the onset of the algebraic tail in the momentum distribution function and the corresponding empirical criterion reported by Hunger \emph{et al.}~[\textit{Phys.~Rev.~E} \textbf{103}, 053204 (2021)]. In the strongly coupled electron liquid regime, our calculations reveal a more complicated non-monotonic convergence towards the $q\to\infty$ limit that is shaped by the spatial structure in the system. We expect our results to be of broad interest for a number of fields including the study of matter under extreme conditions, the development of improved dielectric theories, and the construction of advanced exchange--correlation functionals for thermal density functional theory.