Fourth Order Diffusion Monte Carlo Algorithms for Solving Quantum Many-Body Problems

Abstract

By decomposing the important sampled imaginary time Schr\"odinger evolution operator to fourth order with positive coefficients, we derived a number of distinct fourth order Diffusion Monte Carlo algorithms. These sophisticated algorithms require higher derivatives of the drift velocity and local energy and are more complicated to program. However, they allowed very large time steps to be used, converged faster with lesser correlations, and virtually eliminated the step size error. We demonstrated the effectiveness of these quartic algorithms by solving for the ground state properties of bulk liquid helium.