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

Abstract

We study the topological quantum phase transition in the 2-D Kitaev honeycomb model by making use of the square root of the quantum Jensen–Shannon divergence and find that the square root of the quantum Jensen–Shannon divergence exhibits singular behaviors at the critical point of quantum phase transition. The scaling behaviors of the square root of the quantum Jensen–Shannon divergence are also examined from the first-order derivatives, and we demonstrate that the square root of the quantum Jensen–Shannon divergence obeys universal finite-size scaling laws. Furthermore, we explore the performance of quantum discord and the relative entropy coherence of the system. It is shown that quantum discord and relative entropy coherence display similar critical behaviors, and the square root of the quantum Jensen–Shannon divergence and quantum discord can serve as good indicators for quantum phase transitions.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11274274) and the Fundamental Research Funds for the Central Universities (Grant Nos. 2017FZA3005 and 2016XZZX002-01).

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Correspondence to Jing-Bo Xu.

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Chen, Q., Zhang, G., Cheng, J. et al. Topological quantum phase transitions in the 2-D Kitaev honeycomb model. Quantum Inf Process 18, 8 (2019). https://doi.org/10.1007/s11128-018-2115-3

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Keywords

  • Quantum Jensen–Shannon divergence
  • Quantum coherence
  • Quantum discord
  • Quantum phase transition