Generalized Kitaev Spin Liquid model andEmergent Twist Defect

The Kitaev spin liquid model on honeycomb lattice offers an intriguingfeature that encapsulates both Abelian and non-Abelian anyons. Recentstudies suggest that the comprehensive phase diagram of possible gener-alized Kitaev model largely depends on the specific details of the discretelattice, which somewhat deviates from the traditional understanding of"topological" phases. In this paper, we propose an adapted version of theKitaev spin liquid model on arbitrary planar lattices. Our revised modelrecovers the toric code model under certain parameter selections withinthe Hamiltonian terms. Our research indicates that changes in parame-ters 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 theHamiltonian on a standard translationally invariant lattice. Additionally,we illustrate that the creation, movement, and fusion of these defects canbe accomplished through natural time evolution by linearly interpolatingthe static Hamiltonian. These defects demonstrate the Ising anyon fusionrule as anticipated. Our findings hint at possible implementation in ac-tual physical materials owing to a more realistically achievable two-body interaction.