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Quantum spin liquids can be faithfully represented and efficientlycharacterized within the framework of Projected Entangled Pair States (PEPS).Guided by extensive exact diagonalization and density matrix renormalizationgroup calculations, we construct an optimized symmetric PEPS for a SU$(3)_1$chiral spin liquid on the square lattice. Characteristic features are revealedby the entanglement spectrum (ES) on an infinitely long cylinder. In all three$\mathbb{Z}_3$ sectors, the level counting of the linear dispersing modes is infull agreement with SU$(3)_1$ Wess-Zumino-Witten conformal field theoryprediction. Special features in the ES are shown to be in correspondence withbulk anyonic correlations, indicating a fine structure in the holographicbulk-edge correspondence. Possible universal properties of topologicalSU$(N)_k$ chiral PEPS are discussed.

SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS