A crucial basic property of antiferromagnetic insulators with SU(2) spins is that adjacent spins can (and tend to) combine to form singlets, or valence bonds. The classical analog of this fact is that adjacent spins prefer to be antiparallel. These two facts underly much of our thinking about ground states of quantum antiferromagnets.
Ultracold alkaline earth atoms can be used to realize magnetic insulators where a minimum of N spins is required to form a singlet, where N can be as large as 10. These systems belong to a virtually unexplored class of quantum magnets. In this talk, I will show that even the simplest such models on the square lattice hold remarkable surprises.