Quantum critical exponents of a planar antiferromagne

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.