Dynamical response in strongly coupled uniform electron liquids: Observation of plasmon-roton coexistence using nine sum rules, Shannon information entropy, and path-integral Monte Carlo simulations

Abstract

Dynamical properties of uniform electron fluids are studied within a nonperturbative approach consisting in the combination of the self-consistent version of the method of moments (SCMM) involving up to nine sum rules and other exact relations, the two-parameter Shannon information entropy maximization procedure, and the $\mathit{ab}\phantom{\rule{0.28em}{0ex}}\mathit{initio}$ path integral Monte Carlo (PIMC) simulations of the imaginary-time intermediate scattering function. The explicit dependence of the dynamic structure factor (DSF) on temperature and density is studied in a broad realm of variation of the dimensionless parameters ($2\ensuremath{\le}{r}_{s}\ensuremath{\le}36$ and $1\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}8$). When the coupling is strong (${r}_{s}\ensuremath{\ge}16$) we clearly observe a bimodal structure of the excitation spectrum with a lower-energy mode possessing a well pronounced rotonlike feature ($\ensuremath{\theta}\ensuremath{\le}2$) and an additional high-energy branch within the roton region which evolves into the strongly overdamped high-frequency shoulder when the coupling decreases (${r}_{s}\ensuremath{\le}10$). We are not aware of any reconstruction of the DSF at these conditions with the effects of dynamical correlations included here via the intermediate scattering and the dynamical Nevanlinna parameter functions. The standard static-local-field approach fails to reproduce this effect. The reliability of our method is confirmed by a detailed comparison with the recent $\mathit{ab}\phantom{\rule{0.28em}{0ex}}\mathit{initio}$ dynamic local field approach by T. Dornheim et al. [Phys. Rev. Lett. 121, 255001 (2018)] available for high/moderate densities (${r}_{s}\ensuremath{\le}10$). Moreover, within the SCMM we are able to construct the modes' dispersion equation in a closed analytical form and find the decrements (lifetimes) of the quasiparticle excitations explicitly. The physical nature of the revealed modes is discussed. Mathematical details of the method are complemented in Appendix. The proposed approach, due to its rigorous mathematical foundation, can find numerous diverse applications in the physics of Fermi and Bose liquids.