Time step bias improvement in diffusion Monte Carlo simulations

A Makri-Miller approximation to the exact propagator and the improved split-operator propagator proposed by Drozdov are implemented within the diffusion Monte Carlo method for the simulation of boson systems, and confronted with the Trotter formula and with the importance sampling technique. As a preliminary approach, we compute analytically the time step bias of the mean energy for the different propagators in the simple case of the harmonic oscillator. These results indicate the improved split-operator propagator as the most accurate. Simulations on one- and three-dimensional model systems confirm the analytical results showing that this propagator is very efficient in reducing the time step bias, therefore improving the efficiency of the algorithm.