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

Abstract

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 Néel to valence bond solid (VBS) between N=9 and N=10. We follow the Néel-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 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 $\gamma \ll 1$ where the isolated layers undergo continuous Néel-VBS transitions.

6 pages, 5 figures

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• Intrinsic transverse field in frustrated quantum Ising magnets: its physical origin and quantum effects
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• Topological terms on topological defects: a quantum Monte Carlo study
• Numerical studies of various Neel-VBS transitions in SU(N) anti-ferromagnets