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

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 wave-numbers $q<2q_F$, with $q_F$ being the Fermi wave-number. 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 non-linear 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 [T. Dornheim et al., Phys. Rev. Lett. 125, 085001 (2020)].