Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function

TL;DR

This paper introduces a complex-time Quantum Monte Carlo method to accurately compute ground-state dynamic structure functions, improving over traditional imaginary-time approaches by enabling better spectral function inference.

Contribution

The authors develop a novel complex-time Monte Carlo approach using high-order propagators, allowing direct access to real-time correlations in quantum systems.

Findings

Enhanced accuracy in dynamic structure function calculations

Successful application to harmonic and quartic oscillators

Improved spectral function inference over inverse Laplace methods

Abstract

We present a method based on the Path Integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose phase $\delta$ acts as an adjustable parameter. By using high-order approximations for the quantum propagator, it is possible to obtain Monte Carlo data all the way from purely imaginary time to $\delta$ values near the limit of real time. As a consequence, it is possible to infer accurately the spectral functions using simple inversion algorithms. We test this approach in the calculation of the dynamic structure function $S(q,\omega)$ of two one-dimensional model systems, harmonic and quartic oscillators, for which $S(q,\omega)$ can be exactly calculated. We notice a clear improvement in the calculation of the dynamic response with respect to the common approach based on the inverse Laplace transform of the imaginary-time correlation function.