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Since strong quantum fluctuations are essential for the emergence of quantumspin liquids, there have been extensive exploration and identification of spinliquid candidates in spin-$1/2$ systems, while such activities are rare inhigher spin systems. Here we report an example of non-Abelian chiral spinliquid emerging in spin-$3/2$ Heisenberg model on a square lattice. By tuningHeisenberg exchange interaction and scalar chirality interaction, we map out aquantum phase diagram enclosing three conventional magnetic orders and a chiralspin liquid based on density matrix renormalization group studies. The natureof the spin liquid is identified as a long-sought bosonic version ofRead-Rezayi state that supports non-Abelian Fibonacci anyonic statistics,identified by the ground state entanglement spectrum. Significantly, weestablish that the non-Abelian CSL emerges through the enlarged local degreesof freedom and enhanced quantum fluctuations near the classical phaseboundaries of competing magnetic orders. Our numerical discovery of an exoticquantum spin liquid in spin-$3/2$ system suggests a new route for discoveringfractionalized quantum phases in frustrated higher spin magnetic compounds.

Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet