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

7 pages, 6 figures

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