Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
ORAL
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 \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.
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.
*This work is supported in part by NSFC under Grant Nos. 12347107 and 12334003, MOSTC under Grant No. 2021YFA1400100 (HY), the New Cornerstone Science Foundation through the Xplorer Prize, and the Shuimu Fellow Foundation at Tsinghua University.
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Publication: Arxiv: 2404.07261
Presenters
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Zhengzhi Wu
- University of Oxford