Dynamic properties of the warm dense uniform electron gas with the qSTLS dielectric scheme

The recently derived Fourier–Matsubara expansion of imaginary–time correlation functions comprises an exact result of linear response theory for finite-temperature quantum many-body systems. In its density–density version, the expansion facilitates systematic comparisons between quasi-exact \emph{ab initio} path integral Monte Carlo simulations and approximate dielectric formalism schemes at the level of the imaginary–time (density–density) correlation functions and the dynamic Matsubara local field corrections. On this theoretical basis, the dynamic properties of the quantum version of the Singwi–Tosi–Land–Sjölander scheme are analyzed for the paramagnetic warm dense uniform electron gas. The marginal improvement compared to the semi-classical version of the Singwi–Tosi–Land–Sjölander scheme is attributed to the weak Matsubara order dependence of the approximate dynamic Matsubara local field correction. The evaluation of the ideal density response function at the non-interacting occupation numbers is identified to constitute a general deficiency of the dielectric formalism, which calls for a reformulation in future works.