Forward-walking Green's Function Monte Carlo Method for Correlation Functions

Abstract

The forward-walking Green's Function Monte Carlo method is used to compute expectation values for the transverse Ising model in (1 + 1)D, and the results are compared with exact values. The magnetisation M_z and the correlation function p ^z (n) are computed. The algorithm reproduces the exact results, and convergence for the correlation functions seems almost as rapid as for local observables such as the magnetisation. The results are found to be sensitive to the trial wavefunction, however, especially at the critical point.