Monte Carlo Simulation of Quantum Spin Systems

A Monte Carlo method applicable to a class of noncommuting spin variables is developed. The technique relies on a stochastic procedure which simulates the dominant vacuum-to-vacuum graphs of quantum many-body theory. Computational speed is only weakly dependent on the dimensionality of the system and is fast enough to handle large lattices. This method is tested on the $S=\frac{1}{2}$ ferromagnetic Heisenberg model in one, two, and three dimensions and on the $S=\frac{1}{2}$ $\mathrm{XY}$ model in one dimension where exact results are known.