Finite population-size effects in projection Monte Carlo methods

Projection (Green's function and diffusion) MOnte Carlo techniques sample a wave function by a stochastic iterative procedure. These method converge to a stationary distribution which is biased, i.e., differs from the exact ground state wave function. This bias occurs because of the use of population control procedures. We demonstrate that these biased Monte Carlo algorithms lead to a modified effective mass which is equal to the desired mass only in the limit of an infinite population of walkers. In general, the bias for the energy scales as 1/N for a population of walkers of size N and is proportional to the expectation value of the kinetic energy. Finally, we consider various strategies to reduce this bias.