Entanglement properties of the two-dimensional SU(3) Affleck-Kennedy-Lieb-Tasaki state

Two-dimensional (spin-2) Affleck-Kennedy-Lieb-Tasaki (AKLT) type valence bond solids on a square lattice are known to be symmetry-protected topological (SPT) gapped spin liquids [S. Takayoshi, P. Pujol, and A. Tanaka Phys. Rev. B 94, 235159 (2016)]. Using the projected entangled pair state framework, we extend the construction of the AKLT state to the case of SU(3), relevant for cold atom systems. The entanglement spectrum is shown to be described by an alternating SU(3) chain of "quarks" and "antiquarks", subject to exponentially decaying (with distance) Heisenberg interactions, in close similarity with its SU(2) analog. We discuss the SPT feature of the state.