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 functions 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 areas satisfied a sum rule. Additionally, as a function of wave number, the peak positions followed the correct dispersion relation. For a double-well oscillator, we demonstrated that 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 five to ten 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. © 1996 The American Physical Society.