Density Functional Theory Perspective on the Nonlinear Response of Correlated Electrons across Temperature Regimes

Abstract

We explore a new formalism to study the nonlinear electronic density response based on Kohn–Sham density functional theory (KS-DFT) at partially and strongly quantum degenerate regimes. It is demonstrated that the KS-DFT calculations are able to accurately reproduce the available path integral Monte Carlo simulation results at temperatures relevant for warm dense matter research. The existing analytical results for the quadratic and cubic response functions are rigorously tested. It is demonstrated that the analytical results for the quadratic response function closely agree with the KS-DFT data. Furthermore, the performed analysis reveals that currently available analytical formulas for the cubic response function are not able to describe simulation results, neither qualitatively nor quantitatively, at small wavenumbers q < 2 q F , with q F being the Fermi wavenumber. The results show that KS-DFT can be used to describe warm dense matter that is strongly perturbed by an external field with remarkable accuracy. Furthermore, it is demonstrated that KS-DFT constitutes a valuable tool to guide the development of the nonlinear response theory of correlated quantum electrons from ambient to extreme conditions. This opens up new avenues to study nonlinear effects in a gamut of different contexts at conditions that cannot be accessed with previously used path integral Monte Carlo methods.

Ab Initio Static Exchange–Correlation Kernel across Jacob’s Ladder without Functional Derivatives

“…The presented idea is not limited to electronic pair correlations. A gradual increase in the amplitude A of the external harmonic perturbation gives one straightforward access to the nonlinear electronic density response ( 20 , 57 , 94 ) of any given system, which, in turn, is directly connected to higher-order correlation functions between three and more electrons. 95 In other words, the presented approach can give one access to the full hierarchy of many-electron correlations within the framework of DFT, and without any additional external input.…”

Spin-resolved density response of the warm dense electron gas

“…We are convinced that our study opens up a number of possibilities for future investigations. i) Accurate results for the spin-resolved density response can be used to benchmark existing approximations and may guide the further development of new, improved dielectric theories [59,60,88,89,137,138]; ii) Our new insights into the interplay of the spin-resolved components of the density response will constitute an important basis for future investigations of matter in an external magnetic field [27]; iii) The practical manifestation of the effective electronelectron attraction [12] in the UEG density response deserves further exploration. This might include the study of spin-resolved pair alignment [9], the possible formation of a charge-and spin-density-wave [3,139], and its potential connection to superconductivity [11].…”

Linear-response time-dependent density functional theory approach to warm dense matter with adiabatic exchange--correlation kernels

“…From a computational point of view, an alternative to the LR-TDDFT is to use a direct perturbation by an external field to measure the density response function connecting the perturbing field with the density change induced by it [48][49][50]. These different formulations and methods for a dynamic density response function have been actively used in the WDM studies [39,[51][52][53][54]. However, in many aspects, the connection between them had not been clearly formulated and understood.…”

“…WDM, dense plasmas, and liquid metals. This method is based on the direct perturbation of the system by a static harmonic potential [18,[35][36][37][38][39]. The difference in the density between perturbed and unperturbed cases allows one to extract the static density response function.…”