${\mathbb{Z}}_2$ spin liquids in the higher spin-$S$ Kitaev honeycomb model: An exact deconfined ${\mathbb{Z}}_2$ gauge structure in a non-integrable model

Abstract

The higher spin Kitaev model prominently features the extensive locally conserved quantities the same as the spin-$1/2$ Kitaev honeycomb model, although it is not exactly solvable. It remains an open question regarding the physical meaning of these conserved quantities in the higher spin model. In this Letter, by introducing a Majorana parton construction for a general spin-$S$ we uncover that these conserved quantities are exactly the ${\mathbb{Z}}_2$ gauge fluxes in the general spin-$S$ model, including the case of spin-$1/2$. Particularly, we find an even-odd effect that the ${\mathbb{Z}}_2$ gauge charges are fermions in the half integer spin model, but are bosons in the integer spin model. We further prove that the fermionic ${\mathbb{Z}}_2$ gauge charges are always deconfined; hence the half integer spin Kitaev model would have non-trivial spin liquid ground states regardless of interaction strengths in the Hamiltonian. The bosonic ${\mathbb{Z}}_2$ gauge charges of the integer spin model, on the other hand, could condense, leading to a trivial product state, and this is indeed the case at the anisotropic limit of the model.

arXiv comment5+4 pages, 3+3 figures, published version

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• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• $Z_2$ flux binding to higher-spin impurities in the Kitaev spin liquid
• Chiral spin state and nematic ferromagnet in the spin-1 Kitaev-$\Gamma$ model
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
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• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Chiral spin liquid in a generalized Kitaev honeycomb model with ${\mathbb{Z}}_4$ 1-form symmetry
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems
• Even-odd effect in multilayer Kitaev honeycomb magnets
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality