Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

Abstract

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 $1/\ensuremath{\xi}=2\text{ }{\text{sinh}}^{\ensuremath{-}1}[\sqrt{2{J}_{z}\ensuremath{-}1}/(1\ensuremath{-}{J}_{z})]$, which diverges around the critical point ${J}_{z}={(1/2)}^{+}$.