Auxiliary-field Monte Carlo for quantum spin and boson systems

We describe an algorithm for the numerical simulation of quantum spin and boson systems. The method is based on the Trotter decomposition in imaginary time and a decoupling by auxiliary Ising spins. It can be applied, in principle, to arbitrary (random) spin systems, however, in general it suffers from the ''minus-sign problem.'' This problem is absent in the case of the Ising model in a transverse field in arbitrary dimensions and geometries. We show test results for the spin-1/2 XY model, the one-dimensional transverse Ising model with disorder, and the phase transition induced by a transverse field in the two-dimensional Ising model. (c) 2000 The American Physical Society.