  In a recent Letter, Dornheim et al. [PRL 125, 085001 (2020)] have
investigated the nonlinear density response of the uniform electron gas in the
warm dense matter regime. More specifically, they have studied the cubic
response function at the first harmonic, which cannot be neglected in many
situations of experimental relevance. In this work, we go one step further and
study the full spectrum of excitations at the higher harmonics of the original
perturbation based on extensive new ab initio path integral Monte Carlo (PIMC)
simulations. We find that the dominant contribution to the density response
beyond linear response theory is given by the quadratic response function at
the second harmonic in the moderately nonlinear regime. Furthermore, we show
that the nonlinear density response is highly sensitive to exchange-correlation
effects, which makes it a potentially valuable new tool of diagnostics. To this
end, we present a new theoretical description of the nonlinear electronic
density response based on the recent effective static approximation to the
local field correction [PRL 125, 235001 (2020)], which accurately reproduces
our PIMC data with negligible computational cost.
