Path-integral Monte Carlo estimator for the dipole polarizability of quantum plasma

We present a path-integral Monte Carlo estimator for calculating the dipole polarizability of interacting Coulomb plasma in the long-wavelength limit, i.e., the optical region. We present comprehensive details and method validation studies for our approach based on dipole imaginary-time autocorrelation functions. The simulation of thermal equilibrium in imaginary time has exact Coulomb interactions and Boltzmann quantum statistics. For reference, we use the Drude model as the long-wavelength limit of the Lindhard response, presenting its analytical continuation into the imaginary time and Matsubara series. We demonstrate great agreement within 1\% between PIMC and the reference model, indicating negligible numerical biases and physical many-body effects in metallic densities. The approach is amenable to nonlinear optical response, quantum confinements, dispersion forces, and to inform applications such as plasmonics and epsilon-near-zero materials.