Laboratoire de Physique Théorique
Toulouse - UMR 5152

Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projected Entangled Pair State (PEPS). Guided by an extensive exact diagonalization (ED) search of chiral spin liquid phase in a short-range interacting SU(3)-symmetric spin system on the square lattice, we construct and optimize a symmetric PEPS ansatz, whose variational energy is remarkably close to ED and density matrix renormalization group results. Characteristic feature of a SU(3)_1 chiral spin liquid, as expected from ED level spectroscopy, is revealed by entanglement spectrum (ES) of the optimized PEPS on an infinitely long cylinder. In all three sectors, the level counting of the linear dispersing modes is in full agreement with SU(3)_1 Wess-Zumino-Witten conformal field theory prediction. Certain special features in ES, e.g. the tripling of the chiral branch in the nonzero Z3 charged sector, are shown to be in correspondence with bulk anyonic correlations, indicating a finer structure in holographic bulk-edge correspondence. Universal properties of topological SU(N)_k chiral PEPS are outlined.