  In recent years, there have been numerous examples of twisted bilayer systems
that host remarkable physical properties that are not found in their untwisted
counterparts. Motivated by this, we study the properties of twisted bilayers of
the Kitaev honeycomb model in the Abelian spin liquid phase. We show that for
strong, short-ranged, interlayer interactions, a super-lattice of non-Abelian
defects forms in the twisted bilayer system. These non-Abelian defects are
wormhole-like genons that allow anyons from one layer to tunnel to the other
layer. We find that when a magnetic field is applied to the system, the low
energy dynamics of the twisted bilayer system can be mapped onto four quantum
Ising models arising from the degrees of freedom localized on the genon
defects. At small twist angles, the Ising models are in a trivial paramagnetic
phase, and at large twist angles, they are in a ferromagnetic phase.
