Model Fermion Monte Carlo with Correlated Pairs
Kalos, Malvin H.
The issues that prevent the development of efficient and stable algorithms for fermion Monte Carlo in continuum systems are reexamined with special reference to the implications of the "plus/minus" symmetry. This is a property of many algorithms that use signed walkers, namely that the dynamics are unchanged when the signs of the walkers are interchanged. Algorithms that obey this symmetry cannot exhibit the necessary stability. Specifically, estimates of the overlap with any antisymmetric test function cannot be bounded away from zero in the limit of many iterations. Within the framework of a diffusion Monte Carlo treatment of the Schroedinger equation, it is shown that this symmetry is easily broken for pairs of walkers while at the same time preserving the correct marginal dynamics for each member of the pair. The key is to create different classes of correlations between members of pairs and to use (at least) two distinct correlations for a pair and for the same pair withthe signs exchanged. The ideas are applied successfully for a class of simplemodel problems in two dimensions.
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