  We present high precision estimates of the exponents of a quantum phase
transition in a planar antiferromagnet. This has been made possible by the
recent development of cluster algorithms for quantum spin systems, the loop
algorithms. Our results support the conjecture that the quantum Heisenberg
antiferromagnet is in the same universality class as the O(3) nonlinear sigma
model. The Berry phase in the Heisenbrg antiferromagnet do not seem to be
relevant for the critical behavior.
