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

TL;DR

This paper develops a new method to extract nonlinear density responses from imaginary-time correlation functions using ab initio path integral Monte Carlo simulations, enabling efficient analysis of warm dense electron gases and potential three-body dynamic effects.

Contribution

It introduces relations between nonlinear density responses and generalized imaginary-time correlation functions, extending PIMC capabilities beyond linear response analysis.

Findings

Accurate nonlinear density response calculations for warm dense electron gas.

Established relation between cubic ITCF and triple dynamic structure factor.

Validated approach with results consistent with previous, more computationally intensive methods.

Abstract

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