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

TL;DR

This paper constructs a symmetric PEPS representation of a SU(3)_1 chiral spin liquid on the square lattice, revealing its topological and conformal field theory properties through entanglement spectrum analysis.

Contribution

It introduces an optimized symmetric PEPS for SU(3)_1 chiral spin liquids, connecting entanglement features with bulk anyonic correlations and conformal field theory predictions.

Findings

Entanglement spectrum matches SU(3)_1 Wess-Zumino-Witten theory

ES features correspond to bulk anyonic correlations

Universal properties of topological SU(N)_k chiral PEPS discussed

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 $\mathbb{Z}_3$ 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.