The N\'{e}el-VBS transition in three-dimensional SU($N$) antiferromagnets

TL;DR

This study maps the phase diagram of a three-dimensional SU(N) antiferromagnet, revealing a direct first-order Néel to VBS transition without intermediate spin-liquid phases, across various anisotropies and N values.

Contribution

It provides the first comprehensive analysis of the Néel-VBS transition in 3D SU(N) antiferromagnets, showing the transition is first-order with no evidence of a spin-liquid phase.

Findings

Transition from Néel to VBS occurs between N=9 and N=10.

Transition is first-order across the phase diagram.

No evidence of spin-liquid 'photon' phase or continuous transition.

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 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.