Jiang, F-J; Nyfeler, M; Chandrasekharan, S; Wiese, U-J, *From an antiferromagnet to a valence bond solid: Evidence for a first-order phase transition*,
Journal of statistical mechanics (Online), vol. 2008 no. 2
(2008),
pp. P02009(arXiv:0710.3926.)
[available here], [doi] .
**Abstract:**

*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>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. © 2008 IOP Publishing Ltd.*