Numerical study of the two-dimensional Heisenberg model using a Green function Monte Carlo technique with a fixed number of walkers

We describe in detail a simple and efficient Green function Monte Carlo technique for computing both the ground state energy and the ground state properties by the “forward walking” scheme. The simplicity of our reconfiguration process, used to maintain the walker population constant, allows us to control any source of systematic error in a rigorous and systematic way. We apply this method to the Heisenberg model and obtain accurate and reliable estimates of the ground state energy, the order parameter, and the static spin structure factor $S\left(q\right)\mathrm{}$ for several momenta. For the latter quantity we also find very good agreement with available experimental data on the ${\mathrm{La}}_2{\mathrm{CuO}}_4$ antiferromagnet.