From an antiferromagnet to a valence bond solid: evidence for a first-order phase transition

Using a loop–cluster algorithm we investigate the spin- Heisenberg antiferromagnet on a square lattice with exchange coupling J and an additional four-spin interaction of strength Q. We confirm the existence of a phase transition separating antiferromagnetism at J/Q>J_c/Q from a valence bond solid (VBS) state at J/Q<J_c/Q. Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as 80², we find evidence for a weak first-order phase transition. We also present a detailed study of the antiferromagnetic phase. For J/Q>J_c/Q the staggered magnetization, the spin stiffness and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low-energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at J/Q<J_c/Q and we show that long but finite antiferromagnetic correlations are still present.