Real-Time Dynamics from Imaginary-Time Quantum Monte Carlo Simulations: Tests on Oscillator Chains

TL;DR

This paper develops a Bayesian maximum entropy approach to analytically continue imaginary-time quantum Monte Carlo data into real-time Green's functions, successfully testing on oscillator chains and predicting dynamics over several natural periods.

Contribution

It introduces a novel Bayesian maximum entropy method for real-time dynamics extraction from imaginary-time QMC data, validated on oscillator chains with accurate spectral and dispersion predictions.

Findings

Spectral densities correctly locate peaks and satisfy sum rules.

Dispersion relations are accurately recovered from spectral data.

Real-time dynamics are predictable for 5-10 natural periods.

Abstract

We used methods of Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time Green's function generated in quantum Monte Carlo simulations to obtain the real-time Green's functions. For test problems, we considered chains of harmonic and anharmonic oscillators whose properties we simulated by a hybrid path-integral quantum Monte Carlo method. From the imaginary-time displacement-displacement Green's function, we first obtained its spectral density. For harmonic oscillators, we demonstrated the peaks of this function were in the correct position and their area satisfied a sum rule. Additionally, as a function of wavenumber, the peak positions followed the correct dispersion relation. For a double-well oscillator, we demonstrated the peak location correctly predicted the tunnel splitting. Transforming the spectral densities to real-time Green's functions, we conclude that we can predict the real-time dynamics for length of times corresponding to 5 to 10 times the natural period of the model. The length of time was limited by an overbroadening of the peaks in the spectral density caused by the simulation algorithm.