Computational Studies of $T=0$ Neel-Valence bond solid transitions in two dimensional quantum antiferromagnets

We use Quantum Monte Carlo techniques to study a direct quantum phase transition in two dimensional quantum antiferromagnets between a collinear Neel ordered state and a valence bond solid ordered singlet state. We contrast the strongly first order behavior of the transition in cases where the valence bond solid order is of a ``staggered'' type with the deconfined critical behavior seen in cases where the valence-bond solid order is of a columnar type. In the deconfined case, we find evidence for weak, apparently logarithmic violations of scaling. [References: preprint; Phys. Rev. B 83, 235111 (2011); Phys. Rev. B 83, 134419 (2011); Phys. Rev. B 82, 155139 (2010)]