  We apply continuous similarity transformations (CSTs) to study the
zero-temperature breakdown of long-range ordered quantum antiferromagnets. The
CST flow equations are truncated in momentum space by the scaling dimension so
that all operators with scaling dimension up to two are taken into account. We
determine the quantum phase transition out of the N\'eel-ordered phase in the
unfrustrated square lattice Heisenberg bilayer as well as the quantum melting
of the N\'eel-ordered and columnar phase in the highly frustrated $J_1$-$J_2$
model on the square lattice. In all cases the CST is set up to isolate the
ground state so that the stability of the flow equations, the ground-state
energy, and the sublattice magnetization are used to explore the long-range
ordered phases. We extract quantum-critical points which agree well with values
in the literature. Further, we estimate the associated critical exponents
$\alpha$ and $\beta$ which turns out to be a challenging task for the CST
approach.
