  The spin-S Kitaev model has recently been shown to definitely exhibit
topological order with spin liquid ground states for half-integer spin, but
could be trivially gapped insulators for integer spin. This interesting
"even-odd" effect is largely due to the fermionic (bosonic) $\mathbb{Z}_2$
gauge charges for half-integer (integer) spin. In this Letter, we theoretically
show that a spin-S Yao-Lee model (a spin-orbital model with SU(2) spin-rotation
symmetry) possesses exact deconfined fermionic $\mathbb{Z}_2$ gauge charges for
any spin (both integer and half integer spin), which implies a
topologically-nontrivial quantum spin-orbital liquid (QSOL) ground state
regardless of the value of the spin quantum number. We further study the
easy-axis limit of the spin-1 Yao-Lee model which can be solved in a controlled
perturbative way and show that it exhibits a gapless QSOL ground state, which
can even host a non-Abelian topological order by further considering
time-reversal breaking interactions to gap out the Dirac cones of the gapless
QSOL.
