Classical Correlation-Length Exponent in Non-Universal Quantum Phase Transition of Diluted Heisenberg Antiferromagnet

Critical behavior of the quantum phase transition of a site-diluted Heisenberg antiferromagnet on a square lattice is investigated by means of the quantum Monte Carlo simulation with the continuous-imaginary-time loop algorithm. Although the staggered spin correlation function decays in a power law with the exponent definitely depending on the spin size $S$, the correlation-length exponent is classical, i.e., $\nu=4/3$. This implies that the length scale characterizing the non-universal quantum phase transition is nothing but the mean size of connected spin clusters.