Abstract
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 $\mathrm{XY}$ model, the one-dimensional transverse Ising model with disorder, and the phase transition induced by a transverse field in the two-dimensional Ising model.
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