We study exactly both the ground-state fidelity susceptibility and bond-bond correlation function in the Kitaev honeycomb model. Our results show that the fidelity susceptibility can be used to identify the topological phase transition from a gapped $A$ phase with Abelian anyon excitations to a gapless $B$ phase with non-Abelian anyon excitations. We also find that the bond-bond correlation function decays exponentially in the gapped phase, but algebraically in the gapless phase. For the former case, the correlation length is found to be $1/\xi =2{\text{sinh}}^{-1}\left[\sqrt{2J_z-1}/\left(1-J_z\right)\right]$, which diverges around the critical point $J_z={\left(1/2\right)}^{+}$.

• Received 27 March 2008

DOI:https://doi.org/10.1103/PhysRevA.78.012304