Z2 spin liquids in the Higher spin Kitaev Honeycomb model: an exact Z2 gauge structure in a non-integrable model

The higher spin Kitaev models have extensive locally conserved quantities the same as the spin-1/2 Kitaev honeycomb model, although they are not exactly solvable. In this talk, I will present their exact gauge structure by introducing a Majorana parton construction for a general spin-S. These conserved quantities are exactly the Z2 gauge fluxes. Particularly, we find an even-odd effect that the Z2 gauge charges are fermions in the half integer spin model, but are bosons in the integer spin model. We further prove that the fermionic Z2 gauge charges are always deconfined; hence, the half integer spin Kitaev model would have nontrivial spin liquid ground states regardless of interaction strengths in the Hamiltonian. The bosonic Z2 gauge charges of the integer spin model could condense, leading to a trivial product state, and this is indeed the case at the anisotropic limit of the model.