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

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.