Density Response of the Warm Dense Electron Gas beyond Linear Response Theory: Excitation of Harmonics

Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization

“…In particular, this allows for thermal density functional theory simulations on the level of the local density approximation [49,50], and constitutes the basis for the development of more sophisticated functionals that explicitly take into account the temperature [69,70]. Further progress on the UEG at WDM conditions includes the characterization of linear-response properties such as the static local field correction [71][72][73][74], numerical and theoretical results for the nonlinear electronic density response [75,76], and even the study of dynamic quantities based on the analytic continuation of imaginary-time correlation functions [9,71,[77][78][79].…”

The Relevance of Electronic Perturbations in the Warm Dense Electron Gas

“…Furthermore, Eq. ( 1) has been used to rigorously examine various fundamental physical properties of the electronic structure in WDM, such as the local field correction (LFC) [71][72][73][74] and the non-linear response 70,75,76 that are used to describe XRTS signals. Moreover, it turns out that the UEG model provides an excellent description of many electronic properties in WDM, because the electron-ion coupling can be relatively weak 75,77,78 .…”

Nonlinear density response from imaginary-time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas

“…Unfortunately, the relations (1)-( 3) have hitherto been limited to the linear response regime, i.e., the limit of a weak perturbation whose effect can be described in first-order of the perturbation strength. This is highly unsatisfactory as nonlinear effects are known to play an important role in many situations, such as the excitation spectrum of graphene [56][57][58], the optical excitation and ionization of atoms [59,60], and state-of-the-art experiments with warm dense matter [61,62]. Therefore, the first PIMC results for the nonlinear density response have been obtained by actually applying an external perturbation to the system and subsequently measuring its response.…”

“…Obviously, this procedure is exceed-ingly demanding as it requires to perform N A ∼ 10 independent PIMC simulations to compute the nonlinear response for a single wave vector q. At the same time, we note that nonlinear effects are substantially more sensitive to exchange-correlation effects [62], which makes exact PIMC simulations all the more important.…”

“…In the present work, we overcome this limitation by presenting analogous relations between density-density ITCFs depending on two and three τ -arguments and the generalized quadratic and cubic static response functions Y (q 1 , q 2 ) and Z (q 1 , q 2 , q 3 ), respectively. As a practical example of high relevance, we carry out simulations of the uniform electron gas (UEG) at warm dense matter conditions and compare the results from our new scheme to previous PIMC data [61,62] that have been obtained from the perturbed electrons gas with substantially larger computational effort. In addition, we outline a strategy for an analytic continuation of these new ITCFs, which, in principle, gives one access to generalized dynamic structure factors involving the time-dependent correlations between three and four particles.…”