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We explore a new formalism to study the nonlinear electronic density responsebased on Kohn-Sham density functional theory (KS-DFT) at partially and stronglyquantum degenerate regimes. It is demonstrated that the KS-DFT calculations areable to accurately reproduce the available path integral Monte Carlo simulationresults at temperatures relevant for warm dense matter research. The existinganalytical results for the quadratic and cubic response functions arerigorously tested. It is demonstrated that the analytical results for thequadratic response function closely agree with the KS-DFT data. Furthermore,the performed analysis reveals that currently available analytical formulas forthe 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 todescribe warm dense matter that is strongly perturbed by an external field withremarkable accuracy. Furthermore, it is demonstrated that KS-DFT constitutes avaluable tool to guide the development of the non-linear response theory ofcorrelated quantum electrons from ambient to extreme conditions. This opens upnew avenues to study nonlinear effects in a gamut of different contexts atconditions that cannot be accessed with previously used path integral MonteCarlo methods [T. Dornheim et al., Phys. Rev. Lett. 125, 085001 (2020)].

Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes