First-order N\'eel-cVBS transition in a model square lattice $S=1$ antiferromagnet

We study the N\'eel to four-fold 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 DCP 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 for a first order transition demonstrating co-existence including double peaked histograms and switching behavior are observed. The sharp contrast from the $S=1/2$ case is remarkable, and is a striking demonstration of the role of the size of the quantum spin in the phase diagram of two dimensional lattice models.