  We discuss ground-state projector simulations of a modified two-dimensional
S=1/2 Heisenberg model in the valence bonds basis. Tuning matrix elements
corresponding to the diagonal and off-diagonal terms in the quantum dimer
model, we show that there is a quantum phase transition from the
antiferromagnet into a columnar valence-bond-solid (VBS). There are no signs of
discontinuities, suggesting a continuous or very weakly first-order transition.
The Z4-symmetric VBS order parameter exhibits an emergent U(1) symmetry as the
phase transition is approached. We extract the associated length-scale
governing the U(1)-Z4 cross-over inside the VBS phase.
