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

Abstract

Using a loop‐cluster algorithm we investigate the spin 12 Heisenberg antiferromagnet on a square lattice with exchange coupling J and a four‐spin interaction of strength Q. We confirm the existence of a phase transition separating antiferromagnetism at J/Q>Jc/Q from a valence bond solid (VBS) state at J/Q<Jc/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>Jc/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<Jc/Q, and we show that long but finite antiferromagnetic correlations are still present.