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

Abstract

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 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.

4 pages+ Supplementary Material, 1 figure

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• Field-induced phase transitions in the Kitaev-Heisenberg model: A sign-problem-free quantum Monte Carlo study and possible application to $\alpha$-RuCl3
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality