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Quantum Information Processing

Topological quantum phase transitions in the 2-D Kitaev honeycomb model

Qi Chen, Guo-Qing Zhang, Jun-Qing Cheng, Jing‐Bo Xu

Published Nov 19, 2018• 13 citations
Publisher
DOI
10.1007/s11128-018-2115-3

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We study reduced fidelity and reduced fidelity susceptibility in the Kitaev honeycomb model. It is shown that the nearest-two-site reduced fidelity susceptibility manifests itself as a peak at the quantum phase transition point, although the one-site reduced fidelity susceptibility vanishes. Our results directly reveal that the reduced fidelity susceptibility can be used to characterize the quantum phase transition in the Kitaev honeycomb model, which suggests that, despite its local nature, the reduced fidelity susceptibility is an accurate marker of the topological phase transition when it is properly chosen.
The Kitaev honeycomb model with a topological phase transition at zero temperature is studied using the quantum-information method. Based on the exact solution of the ground state, the mutual information between two nearest sites and between two bonds with the greatest distance are obtained. It is found that the mutual information shows some singularities at the critical point where the system transits from the gapless phase to the gapped phase. Finite-size effects and scaling behavior are also studied. Our results indicate that the mutual information can serve as a good indicator of the topological phase transition. This is because the mutual information is believed to be able to catch some global correlation properties of the system. Meanwhile, this method has the advantages that the phase transition can be determined easily and the order parameters, which are hard to obtain for some topological phase transitions, are not necessarily known.
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.