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Register a new userThe N{e}el-VBS transition in three-dimensional SU($N$) antiferromagnets
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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 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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In this manuscript we review recent developments in the numerical simulations of bipartite SU(N) spin models by quantum Monte Carlo (QMC) methods. We provide an account of a large family of newly discovered sign-problem free spin models which can be simulated in their ground states on large lattices, containing O(10^5) spins, using the stochastic series expansion method with efficient loop algorithms. One of the most important applications so far of these Hamiltonians are to unbiased studies of quantum criticality between Neel and valence bond phases in two dimensions -- a summary of this body of work is provided. The article concludes with an overview of the current status of and outlook for future studies of the designer Hamiltonians.
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