Kagome model for a ${\mathbb Z}_2$ quantum spin liquid

Understand

We present a study of a simple model antiferromagnet consisting of a sum of nearest neighbor SO($N$) singlet projectors on the Kagome lattice.

• Our model shares some features with the popular $S=1/2$ Kagome antiferromagnet but is specifically designed to be free of the sign-problem of quantum Monte Carlo.
• In our numerical analysis, we find as a function of $N$ a quadrupolar magnetic state and a wide range of a quantum spin liquid.
• A solvable large-$N$ generalization suggests that the quantum spin liquid in our original model is a gapped ${\mathbb Z}_2$ topological phase.