  We use Langevin sampling methods within the auxiliary-field quantum Monte
Carlo algorithm to investigate the phases of the Su-Schrieffer-Heeger model on
the square lattice at the O(4) symmetric point. Based on an explicit
determination of the density of zeros of the fermion determinant, we argue that
this method is efficient in the adiabatic limit. By analyzing dynamical and
static quantities of the model, we demonstrate that a $(\pi,\pi)$ valence bond
solid gives way to an antiferromagnetic phase with increasing phonon frequency.
