Numerical study of the two dimensional Heisenberg model by Green Function Monte Carlo at fixed number of walkers

TL;DR

This paper introduces a simple Green Function Monte Carlo method with forward walking for accurately computing ground state properties of the 2D Heisenberg model, demonstrating good agreement with experimental data.

Contribution

The paper presents a new, efficient Green Function Monte Carlo technique with a straightforward reconfiguration process for systematic error control.

Findings

Accurate estimates of ground state energy and order parameter.

Reliable calculations of static spin structure factor S(q).

Good agreement with experimental data on La2CuO4.

Abstract

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 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(q) for several momenta. For the latter quantity we also find very good agreement with available experimental data on the La2CuO4 antiferromagnet.