  We simulate the spin-1/2 Heisenberg model with a spatially staggered
anisotropy using first principles Monte Carlo method. In particular, the
critical exponents $\beta/\nu$ and $\omega$ associated with the quantum phase
transition induced by dimerization are determined with high precision. Here
$\beta$ and $\nu$ are the exponents related to the magnetization and the
correlation length, respectively. In addition, $\omega$ is the confluent
exponent. With very accurate data of the relevant observables, we first obtain
a value of $\omega$ compatible with the known result in the O(3) universality
class. Further, using either the value of $\omega$ determined here or the
established one in the literature, the exponent $\beta/\nu$ calculated from our
data is in quantitative agreement with the known result $\beta/\nu = 0.519(1)$
as well. Our investigation suggests that the quantum phase transition studied
here is fully consistent with the O(3) universality class.
