SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: A View from Symmetric Projected Entangled Pair States

Ji-Yao Chen, Sylvain Capponi, Alexander Wietek, Matthieu Mambrini, Norbert Schuch, and Didier Poilblanc
Phys. Rev. Lett. 125, 017201 (2020)   Published 2020


Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projected Entangled Pair States (PEPS). Guided by extensive exact diagonalization and density matrix renormalization group calculations, we construct an optimized symmetric PEPS for a SU$(3)_1$ chiral spin liquid on the square lattice. Characteristic features are revealed by 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 in full agreement with SU$(3)_1$ Wess-Zumino-Witten conformal field theory prediction. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence. Possible universal properties of topological SU$(N)_k$ chiral PEPS are discussed.