First-order Néel to columnar valence bond solid transition in a model square-lattice S=1 antiferromagnet

We study the N\'eel to fourfold columnar valence bond solid (cVBS) quantum phase transition in a sign-free $S=1$ square-lattice model. This is the same kind of transition that for $S=1/2$ has been argued to realize the prototypical deconfined critical point. Extensive numerical simulations of the square-lattice $S=1/2$ N\'eel-VBS transition have found consistency with the deconfined critical point scenario with no direct evidence for first-order behavior. In contrast to the $S=1/2$ case, in our quantum Monte Carlo simulations for the $S=1$ model, we present unambiguous evidence for a direct conventional first-order quantum phase transition. Classic signs of a first-order transition demonstrating coexistence including double-peaked histograms and switching behavior are observed. The sharp contrast from the $S=1/2$ case is remarkable; we hypothesize that this is a striking demonstration of the role of the size of the quantum spin in the phase diagram of two-dimensional lattice models.