Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons

The non-integrable higher spin Kitaev honeycomb model has an exact $\mathbb{Z}_2$ gauge structure, which exclusively identifies quantum spin liquid (QSL)

in the half-integer spin Kitaev model. But its constraints for the integer-spin Kitaev model are much limited, and even trivially gapped insulators cannot be excluded. The physical implications of exact $\mathbb{Z}_2$ gauge structure, especially $\mathbb{Z}_2$ fluxes, in integer-spin models remain largely unexplored. In this Letter, we theoretically show that a spin-S Yao-Lee model (a spin-orbital model with SU(2) spin-rotation symmetry) possesses a topologically-nontrivial quantum spin-orbital liquid (QSOL) ground state for \textit{any} spin (both integer and half-integer spin) by constructing exact deconfined fermionic $\mathbb{Z}_2$ gauge charges. We further show that the conserved $\mathbb{Z}_2$ flux can also demonstrate the intriguing spin fractionalization phenomena in the nonabelian topological order phase of the spin-1 Yao-Lee model. Its deconfined $\mathbb{Z}_2$ vortex excitation carries fractionalized spin-$\frac{1}{2}$ quantum number in the low-energy subspace, which is also an nonabelian anyon.

Our exact manifestation of spin fractionalization in an integer-spin model is rather rare in previous studies, and is absent in the Kitaev honeycomb model.