Orateur
Description
The higher-spin Kitaev models possess an extensive set of local conserved quantities, much like the spin-1/2 Kitaev honeycomb model, although they are not exactly solvable. In this talk, I will present the exact gauge structure of the spin-S Kitaev honeycomb model and show that these conserved quantities are precisely the Z2 gauge fluxes. A striking even-odd effect emerges: the Z2 gauge charges are fermionic for half-integer spins, but bosonic for integer spins. We show that the fermionic charges are always deconfined, implying that half-integer-spin Kitaev models necessarily realize nontrivial spin-liquid ground states. In contrast, the bosonic charges in the integer-spin case can condense, leading to a trivial product state, as happens in the anisotropic limit. This distinction is closely tied to an anomaly of the 1-form symmetry. I will also discuss applications to the quadrupolar Kitaev model.
