Model fermion Monte Carlo with correlated pairs. II

Abstract

We study the fundamental challenge of fermion Monte Carlo for continuous systems: the fermion “sign problem.” In particular, we describe methods that depend upon the use of correlated dynamics for ensembles of correlated sets of walkers that carry opposite signs. We explain the concept of marginally correct dynamics, and show that marginally correct dynamics that produce a stable overlap with an antisymmetric trial function give the correct fermion ground state. Many-body harmonic oscillator problems are particularly tractable: their stochastic dynamics permits the use of regular geometric structures for the ensembles, structures that are stable when appropriate correlations are introduced, and avoid the decay of signal-to-noise that is a normal characteristic of the sign problem. This approach may be a guide in the search for algorithmic approaches to calculations of physical interest.