CORRELATED PAIRS IN MODEL FERMION MONTE-CARLO CALCULATIONS

The issues that prevent the development of efficient and stable algori thms for fermion Monte Carlo calculations in continuum systems are ree xamined with special reference to the implications of the ''plus-minus '' symmetry. This is a property of many algorithms that use signed wal kers, namely, that the dynamics are unchanged when the signs of the wa lkers are interchanged. Algorithms that obey this symmetry cannot exhi bit the necessary stability. Specifically, estimates of the overlap wi th any antisymmetric test function cannot be bounded away from zero in the limit of many iterations. Within the framework of a diffusion Mon te Carlo treatment of the Schrodinger 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 a nd for the same pair with signs exchanged. The ideas are applied succe ssfully for a class of simple model problems in two dimensions.