Real-time response from imaginary-time simulation: Hacking quantum statistics with path-integral Monte Carlo

Real-time response from imaginary-time simulation: Hacking quantum statistics with path-integral Monte Carlo Variants of Quantum Monte Carlo (QMC) excel at describing complex quantum statistical problems, such as exact many-body correlations. Unfortunately, most QMC methods operate in imaginary time, which makes estimation of real-time dynamic properties a notorious challenge [1]. Theoretically, the estimation is possible by performing analytic continuation on generalized susceptibilities, or the quantum correlation functions. However, the practical implementation is an ill-posed inversion problem, which defies even the most sophisticated methods. Here we focus on a particular numerical approach: Maximum Entropy [1]. For demonstration, we consider the standard electric field response of small atoms and molecules: static and dynamic multipole polarizability. The polarizability is a fundamental property involved in a plethora of physical models, including infrared activity, optical dispersion, and x-ray scattering. Indeed, the full spectrum of electric field response is often decoupled in the adiabatic approximation. However, we have managed to go beyond the Born–Oppenheimer approximation by using multiscale path-integral Monte Carlo simulation: In a recent work, we present the combined electronic, rovibrational and nonadiabatic effects on the total dynamic polarizability [2]. The results include estimates of the exact multipole spectra, dynamic polarizabilities, and – for the general enjoyment – accurate van der Waals coefficients from first principles. [1] M. Jarrell & J.E. Gubernatis, Bayesian inference and the analytic continuation of imaginary-time quantum {Monte Carlo} data, Physics Reports 269, 133 (1996) [2] J. Tiihonen and I. Kylänpää and T.T. Rantala, Computation of Dynamic Polarizabilities and van der Waals Coefficients from Path-Integral Monte Carlo, Journal of Chemical Theory and Computation 14, 5750 (2018)