Matthew S. Block, Ribhu K. Kaul
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 $\gamma$. In the ``isotropic'' $\gamma=1$ cubic limit, we find a transition from N\'{e}el to valence bond solid (VBS) between $N=9$ and $N=10$. We follow the N\'{e}el-VBS transition to the limiting cases of $\gamma \ll 1 $ (weakly coupled layers) and $\gamma \gg 1$ (weakly coupled chains). Throughout the phase diagram we find a direct {\em first-order} transition from N\'{e}el 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 $\gamma \ll 1$ where the isolated layers undergo continuous N\'{e}el-VBS transitions.
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http://arxiv.org/abs/1205.3530
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