Reweighting estimators for density response in path integral Monte Carlo: Applications to linear, nonlinear, and cross-species density response

We present density response estimators for Monte Carlo simulations that are based on a reweighting procedure, where the samples of an unperturbed multi-component system are used to estimate the properties of a system perturbed by an external harmonic potential. This allows the species-resolved linear and nonlinear static density response to be estimated purely from simulations of the unperturbed system. The method is demonstrated for the uniform electron gas under warm dense matter and strongly coupled conditions using ab initio path integral Monte Carlo simulations. The performance of the method with respect to the number of particles and the number of imaginary time slices is investigated. The scheme is generalized to consider multiple external perturbations, acting on different species and with different wavenumbers, giving one access to additional cross-species density response functions and the complete quadratic response function resolved for both wavenumber arguments through mode coupling. The flexibility of the methodology opens the possibility to investigate numerous new density response properties to further advance our understanding of interacting quantum many-body systems across a broad range of applications.