Néel-VBS transition in three-dimensional SU(N) antiferromagnets

We present results for the phase diagram of an SU(N) generalization of the Heisenberg antiferromagnet on a bipartite three-dimensional anisotropic cubic (tetragonal) lattice as a function of N and the lattice anisotropy γ. In the "isotropic" γ=1 cubic limit, we find a transition from Néel to valence bond solid (VBS) between N=9 and N=10. We follow the Néel-VBS transition to the limiting cases of γ 1 (weakly coupled layers) and γ 1 (weakly coupled chains). Throughout the phase diagram we find a direct first-order transition from Néel at small N to VBS at large N. In the three-dimensional models studied here, we find no evidence for either an intervening spin-liquid "photon" phase or a continuous transition, even close to the limit γ 1 where the isolated layers undergo continuous Néel-VBS transitions.