Survey of exact N-body decompositions of stochastic scalar-Jastrow–Hartree form

Abstract

The quantum N-body dynamics problem with pairwise interactions can be exactly decomposed into the average of N stochastically evolving 1-body problems, thereby eliminating the usual exponential scaling of computational costs. Unfortunately, the variance in such averages can be large leading to slow Monte Carlo convergence. In addition, norm preserving decompositions are available only for identical fermions or bosons. Here we introduce a family of decompositions of scalar-Jastrow–Hartree form which can be applied to electronic structure and many molecular dynamics problems. We also discuss their convergence properties and test a few such methods on the vibrational stretching mode dynamics of CH 4. Finally, we explain how the Monte Carlo convergence problem can be completely eliminated via the introduction of a perfect control variate.