Exact spontaneous plaquette ground states for high-spin ladder models

We study the exchange physics in high spin Mott insulating systems with $S=3/2$ which is realizable in ultracold atomic systems. The high symmetry of SO(5) or SU(4) therein renders stronger quantum fluctuations than the usual spin-1/2 systems. A spontaneous plaquette ground state without any site and bond spin orders is rigorously proved in a ladder spin-3/2 model, whose topological excitations exhibit fractionalization behavior. The generalization to the SU(N) plaquette state is also investigated.