Second roton feature in the strongly coupled electron liquid

TL;DR

This paper uses advanced Monte Carlo simulations to analyze the dynamic properties of the electron gas at various densities, revealing a second roton feature indicative of incipient phonon dispersion and providing benchmarks for future research.

Contribution

It presents the first clear identification of a second roton in the strongly coupled electron liquid using ab initio PIMC methods and analytic continuation techniques.

Findings

Detection of a second roton at high coupling strength

Identification of incipient phonon dispersion

Provision of benchmark data for theoretical models

Abstract

We present extensive \emph{ab initio} path integral Monte Carlo (PIMC) results for the dynamic properties of the finite temperature uniform electron gas (UEG) over a broad range of densities, $2\leq r_s\leq300$. We demonstrate that the direct analysis of the imaginary-time density--density correlation function (ITCF) allows for a rigorous assessment of the density and temperature dependence of the previously reported roton-type feature [T.~Dornheim, \emph{Phys.~Rev.~Lett.}~\textbf{121}, 255001 (2018)] at intermediate wavenumbers. We clearly resolve the emergence of a second roton at the second harmonic of the original feature for $r_s\gtrsim100$, which we identify as an incipient phonon dispersion. Finally, we use our highly accurate PIMC results for the ITCF as the basis for an analytic continuation to compute the dynamic structure factor, which additionally substantiates the existence of the second roton in the strongly coupled electron liquid. Our investigation further elucidates the complex interplay between quantum delocalization and Coulomb coupling in the UEG. All PIMC results are freely available online and provide valuable benchmarks for other theoretical methodologies and approximations.