  We study the quantum phase transition between Abelian and non-Abelian phases
in an extended Kitaev spin model on the honeycomb lattice, where the periodic
boundary condition is applied by placing the lattice on a torus. Our analytical
results show that this spin model exhibits a continuous quantum phase
transition. Also, we reveal the relationship between bipartite entanglement and
the ground-state energy. Our approach directly shows that both the entanglement
and the ground-state energy can be used to characterize the topological quantum
phase transition in the extended Kitaev spin model.
