Su(3) Trimer Resonating-Valence-Bond State On The Square Lattice

We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state with C-4v point-group symmetry on the square lattice. By devising a projected entangled-pair state representation, we show that all (connected) correlation functions between local operators in this SU(3) tRVB state decay exponentially, indicating its gapped nature. We further calculate the modular S and T matrices by constructing all nine topological sectors on a torus and establish the existence of Z(3) topological order in this SU(3) tRVB state.