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

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

2000-09-22

arxiv.org/abs/nucl-th/0009068v1

Int.J.Mod.Phys. B15 (2001) 1752-1755

Physics

Nuclear Physics

Nuclear Theory

23 pages and 6 figures

Scientific paper

10.1142/S0217979201006306

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.

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