Langevin dynamics simulations of the two-dimensional Su-Schrieffer-Heeger model

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.