  The Kitaev spin liquid model on honeycomb lattice offers an intriguing
feature that encapsulates both Abelian and non-Abelian anyons. Recent studies
suggest that the comprehensive phase diagram of possible generalized Kitaev
model largely depends on the specific details of the discrete lattice, which
somewhat deviates from the traditional understanding of "topological" phases.
In this paper, we propose an adapted version of the Kitaev spin liquid model on
arbitrary planar lattices. Our revised model recovers the toric code model
under certain parameter selections within the Hamiltonian terms. Our research
indicates that changes in parameters can initiate the emergence of holes,
domain walls, or twist defects. Notably, the twist defect, which presents as a
lattice dislocation defect, exhibits non-Abelian braiding statistics upon
tuning the coefficients of the Hamiltonian on a standard translationally
invariant lattice. Additionally, we illustrate that the creation, movement, and
fusion of these defects can be accomplished through natural time evolution by
linearly interpolating the static Hamiltonian. These defects demonstrate the
Ising anyon fusion rule as anticipated. Our findings hint at possible
implementation in actual physical materials owing to a more realistically
achievable two-body interaction.
