We introduce a simple model of SO(N) spins with two-site interactions which is amenable to quantum Monte Carlo studies without a sign problem on nonbipartite lattices. We present numerical results for this model on the two-dimensional triangular lattice where we find evidence for a spin nematic at small N, a valence-bond solid at large N, and a quantum spin liquid at intermediate N. By the introduction of a sign-free four-site interaction, we uncover a rich phase diagram with evidence for both first-order and exotic continuous phase transitions.
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This research was supported in part by National Science Foundation Grant No. DMR-1056536.
Kaul, Ribhu K., "Spin Nematics, Valence-Bond Solids, and Spin Liquids in SO(N) Quantum Spin Models on the Triangular Lattice" (2015). Physics and Astronomy Faculty Publications. 376.