Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study

Abelian and non-Abelian topological phases exhibiting protected chiral edge modes are ubiquitous in the realm of the Fractional Quantum Hall (FQH) effect. Here, we investigate a spin-1 Hamiltonian on the square lattice which could, potentially, host the spin liquid analog of the (bosonic) non-Abelian Moore-Read FQH state, as suggested by Exact Diagonalisation of small clusters. Using families of fully SU(2)-spin symmetric and translationally invariant chiral Projected Entangled Pair States (PEPS), variational energy optimization is performed using infinite-PEPS methods, providing good agreement with Density Matrix Renormalisation Group (DMRG) results. A careful analysis of the bulk spin-spin and dimer-dimer correlation functions in the optimized spin liquid suggests that they exhibit long-range "gossamer tails". We argue these tails are finite-$D$ artifacts of the chiral PEPS, which become irrelevant when the PEPS bond dimension $D$ is increased. From the investigation of the entanglement spectrum, we observe sharply defined chiral edge modes following the prediction of the SU(2)$_2$ Wess-Zumino-Witten theory and exhibiting a conformal field theory (CFT) central charge $c=3/2$, as expected for a Moore-Read chiral spin liquid. We conclude that the PEPS formalism offers an unbiased and efficient method to investigate non-Abelian chiral spin liquids in quantum antiferromagnets.