Ab initio density response and local field factor of warm dense hydrogen

We present quasi-exact ab initio path integral Monte Carlo(PIMC)results for the partial static density responses and local field factors of hydrogen in the warm dense matter regime,from solid density conditions to the strongly compressed case.The full dynamic treatment of electrons and protons on the same footing allows us to rigorously quantify both electronic and ionic exchange–correlation effects in the system,and to compare the results with those of earlier incomplete models such as the archetypal uniform electron gas or electrons in a fixed ion snapshot potential that do not take into account the interplay between the two constituents.The full electronic density response is highly sensitive to electronic localization around the ions,and our results constitute unambiguous predictions for upcoming X-ray Thomson scattering experiments with hydrogen jets and fusion plasmas.All PIMC results are made freely available and can be used directly for a gamut of applications,including inertial confinement fusion calculations and the modeling of dense astrophysical objects.Moreover,they constitute invaluable benchmark data for approximate but computationally less demanding approaches such as density functional theory or PIMC within the fixed-node approximation.

Physical insights from imaginary-time density–density correlation functions

An accurate theoretical description of the dynamic properties of correlated quantum many-body systems,such as the dynamic structure factor S(q,ω),is important in many fields.Unfortunately,highly accurate quantum Monte Carlo methods are usually restricted to the imaginary time domain,and the analytic continuation of the imaginary-time density–density correlation function F(q,τ)to real frequencies is a notoriously hard problem.Here,it is argued that often no such analytic continuation is required because by definition,F(q,τ)contains the same physical information as does S(q,ω),only represented unfamiliarly.Specifically,it is shown how one can directly extract key information such as the temperature or quasi-particle excitation energies from theτdomain,which is highly relevant for equation-of-state measurements of matter under extreme conditions[T.Dornheim et al.,Nat.Commun.13,7911(2022)].As a practical example,ab initio path-integral Monte Carlo results for the uniform electron gas(UEG)are considered,and it is shown that even nontrivial processes such as the roton feature of the UEG at low density[T.Dornheim et al.,Commun.Phys.5,304(2022)]are manifested straightforwardly in F(q,τ).A comprehensive overview is given of various useful properties of F(q,τ)and how it relates to the usual dynamic structure factor.In fact,working directly in theτdomain is advantageous for many reasons and opens up multiple avenues for future applications.