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

References in corpus (9)

• "Deconfined" quantum critical points
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Three dimensional resonating valence bond liquids and their excitations
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Monopoles in CP(N-1) model via the state-operator correspondence
• Valence bond solid phases in a cubic antiferromagnet

Cited by in corpus (1)

• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure