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The \emph{ab initio} path integral Monte Carlo (PIMC) approach is one of themost successful methods in quantum many-body theory. A particular strength ofthis method is its straightforward access to imaginary-time correlationfunctions (ITCF). For example, the well-known density-density ITCF$F(\mathbf{q},\tau)$ allows one to estimate the linear response of a givensystem for all wave vectors $\mathbf{q}$ from a single simulation of theunperturbed system. Moreover, it constitutes the basis for the reconstructionof the dynamic structure factor $S(\mathbf{q},\omega)$ -- a key quantity instate-of-the-art scattering experiments. In this work, we present analogousrelations between the nonlinear density response in quadratic and cubic orderof the perturbation strength and generalized ITCFs measuring correlationsbetween up to four imaginary-time arguments. As a practical demonstration ofour new approach, we carry out simulations of the warm dense electron gas andfind excellent agreement with previous PIMC results that had been obtained withsubstantially larger computational effort. In addition, we give a relationbetween a cubic ITCF and the triple dynamic structure factor$S(\mathbf{q}_1,\omega_1;\mathbf{q}_2,\omega_2)$, which evokes the enticingpossibility to study dynamic three-body effects on an \emph{ab initio} level.

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