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

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. Unlike the conventional dynamic structure factor in reciprocal space, our approach is based on the real-space dipole autocorrelation function and is suited for long wavelengths and small cell sizes, including finite clusters. The imaginary-time simulation of thermal equilibrium has exact Coulomb interactions and Boltzmann quantum statistics. For reference, we demonstrate analytic continuation of the Drude model into the imaginary time and Matsubara series, showing perfect agreement with our data within ranges of finite temperatures and densities. Method parameters, such as the finite time-step and finite-size effects prove only modestly significant. Our method, here carefully validated against an exactly solvable reference, remains amenable to more interesting domains in higher-order optical response, quantum confinements and quantum statistical effects, and applications in plasmonics, heterogeneous plasmas and nonlinear optics, such as epsilon-near-zero materials.