A fourth order diffusion monte carlo algorithm for solving quantum many-body problems

We derive and numerically implement a fourth order Diffusion Monte Carlo algorithm for solving quantum many-body problems. The method uses a factorization of the imaginary time propagator in terms of the usual local energy and Langevin operators as well as an additional pseudo-potential consisting of the double commutator [EL, [L, EL]]. A new factorization of the propagator of the Fokker-Planck equation enables us to implement the Langevin algorithm to the necessary fourth order. We achieve this by the addition of correction terms to the drift steps and the use of a position-dependent Gaussian random walk. We present exact analytical results for a three dimensional harmonic oscillator and numerical results for a Morse potential. We demonstrate that in the physical case of bulk liquid helium and helium droplets, the systematic step size errors are indeed fourth order over a wide range of step sizes.