PROJECTION MONTE-CARLO METHODS - AN ALGORITHMIC ANALYSIS

Projection methods such as Green's function and diffusion Monte Carlo are commonly used to calculate the leading eigenvalue and eigenvector of operators or large matrices. They thereby give access to ground sta te properties of quantum systems, and finite temperature properties of classical statistical mechanical systems having a transfer matrix. Th e basis of these approaches is a stochastic application of the power m ethod in which a ''projection'' operator is applied iteratively. For t he systematic errors to be small, the number of iterations must be lar ge; however, in that limit, the statistical errors grow tremendously. We present an analytical study of the main variance reduction methods used for dealing with this problem. In particular, we discuss the cons equences of guiding, replication, and population control on statistica l and systematic errors.