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We discuss a projector Monte Carlo method for quantum spin models formulatedin the valence bond basis, using the S=1/2 Heisenberg antiferromagnet as anexample. Its singlet ground state can be projected out of an arbitrary basisstate as the trial state, but a more rapid convergence can be obtained using agood variational state. As an alternative to first carrying out a timeconsuming variational Monte Carlo calculation, we show that a very good trialstate can be generated in an iterative fashion in the course of the simulationitself. We also show how the properties of the valence bond basis enablecalculations of quantities that are difficult to obtain with the standard basisof Sz eigenstates. In particular, we discuss quantities involvingfinite-momentum states in the triplet sector, such as the dispersion relationand the spectral weight of the lowest triplet.

Monte Carlo Simulations of Quantum Spin Systems in the Valence Bond Basis