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Using a loop-cluster algorithm we investigate the spin 1/2 Heisenbergantiferromagnet on a square lattice with exchange coupling $J$ and anadditional four-spin interaction of strength $Q$. We confirm the existence of aphase transition separating antiferromagnetism at $J/Q > J_c/Q$ from a valencebond solid (VBS) state at $J/Q < J_c/Q$. Although our Monte Carlo data areconsistent with those of previous studies, we do not confirm the existence of adeconfined quantum critical point. Instead, using a flowgram method on latticesas 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 spinwavevelocity of the antiferromagnet are determined by fitting Monte Carlo data toanalytic results from the systematic low-energy effective field theory formagnons. 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 arestill present.

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