SU(3)_{1} Chiral Spin Liquid on the Square Lattice: A View from Symmetric Projected Entangled Pair States.

Ji-Yao Chen,Norbert Schuch,Didier Poilblanc,Matthieu Mambrini,Alexander Wietek,Sylvain Capponi

doi:10.1103/physrevlett.125.017201

Abstract

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 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.

Highlights

Introduction.—Quantum spin liquids are entangled states of matter in interacting spin systems, supporting fractionalized excitations [1,2,3]
To establish the relevance of our symmetric projected entangled pair states (PEPS) ansatz for the model (1), we compare the PEPS energy density with that obtained by exact diagonalization (ED) on several tori up to size Ns 1⁄4 24 and by the density matrix renormalization group (DMRG) method [52,53,54] on various finite cylinders, whose details can be found in the Supplemental Material [34]
Entanglement spectrum.—To get further insight into the nature of the chiral spin liquids (CSL) phase, we explore the properties of our symmetric PEPS, where the Z3 gauge symmetry implies topological degeneracy on closed manifolds

Summary

Introduction

Introduction.—Quantum spin liquids are entangled states of matter in interacting spin systems, supporting fractionalized excitations [1,2,3]. SUð3Þ1 Chiral Spin Liquid on the Square Lattice: A View from Symmetric Projected Entangled Pair States

Results

Conclusion