PROJECTION MONTE CARLO METHODS: AN ALGORITHMIC ANALYSIS

Abstract

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 state properties of quantum systems, and finite temperature properties of classical statistical mechanical systems having a transfer matrix. The basis of these approaches is a stochastic application of the power method in which a "projection" operator is applied iteratively. For the systematic errors to be small, the number of iterations must be large; 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 consequences of guiding, replication, and population control on statistical and systematic errors.