Sign problem in Monte Carlo simulations of frustrated quantum spin systems

We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semifrustrated'' systems Heisenberg models with ferromagnetic couplings Jₙ (r) <0 along the z axis and antiferromagnetic couplings Jₗₘ (r) =-Jₙ (r) in the xy plane, for arbitrary distances r, the sign problem present for algorithms operating in the z basis can be solved within a recent ``operator-loop'' formulation of the stochastic series expansion method a cluster algorithm for sampling the diagonal matrix elements of the power series expansion of exp (-) to all orders. The solution relies on the identification of operator loops which change the configuration sign when updated (``merons'') and is similar to the meron-cluster algorithm recently proposed by Chandrasekharan and Wiese for solving the sign problem for a class of fermion models Phys. Rev. Lett. 83, 3116 (1999). Some important expectation values, e. g. , the internal energy, can be evaluated in the subspace with no merons, where the weight function is positive definite. Calculations of other expectation values require sampling of configurations with only a small number of merons (typically zero or two), with an accompanying sign problem which is not serious. We also discuss problems which arise in applying the meron concept to more general quantum spin models with frustrated interactions.