Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin- $\frac{1}{2}$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin- $\frac{3}{2}$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in a spin- $\frac{3}{2}$ system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-$\frac{1}{2}$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin-$\frac{3}{2}$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in a spin-$\frac{3}{2}$ system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.

arXiv:2212.14223Physical review. B./Physical review. BJul 17, 20234 citations

Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-

\frac{1}{2}

systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin-

\frac{3}{2}

Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in a spin-

\frac{3}{2}

system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.