From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition

Using a loop-cluster algorithm we investigate the spin 1/2 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 $80^2$, 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.