GENERALIZATION OF THE FORTUIN-KASTELEYN TRANSFORMATION AND ITS APPLICATION TO QUANTUM SPIN SIMULATIONS

We generalize the Fortuin-Kasteleyn (FK) cluster representation of the partition function of the Ising model to represent the partition func tion of quantum spin models with an arbitrary spin magnitude in arbitr ary dimensions. This generalized representation enables us to develop a new cluster algorithm for the simulation of quantum spin systems by the worldline Monte Carlo method. Because the Swendsen-Wang algorithm is based on the FK representation, the new cluster algorithm naturally includes it as a special case. As well as the general description of the new representation, we present an illustration of our new algorith m for some special interesting cases: the Ising model, the antiferroma gnetic Heisenberg model with S=1, and a general Heisenberg model. The new algorithm is applicable to models with any range of the exchange i nteraction, any lattice geometry, and any dimensions.