Disordered groundstate phase of the SU(N) Heisenberg model with four-column representation

We study the SU(N) Heisenberg interaction with four column representation on the square lattice. We find that the small-N Néel phase disappears for N ≥ 20, where there is no evidence of any order. This is consistent with the large-N theory which predicts a ``2d AKLT'' state that breaks no symmetries of the Hamiltonian in the bulk. Akin to AKLT state in 1d, this state has unpaired spins at the boundaries which form an SU(N) spin chain along both the x and y edges of the square lattice. We find that this spin chain spontaneously breaks translational symmetry along the four edges and forms a valence bond ordered chain.