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Quantum correlation and quantum phase transition in the one-dimensional extended Ising model

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Abstract

Quantum phase transitions can be understood in terms of Landau’s symmetry-breaking theory. Following the discovery of the quantum Hall effect, a new kind of quantum phase can be classified according to topological rather than local order parameters. Both phases coexist for a class of exactly solvable quantum Ising models, for which the ground state energy density corresponds to a loop in a two-dimensional auxiliary space. Motivated by this we study quantum correlations, measured by entanglement and quantum discord, and critical behavior seen in the one-dimensional extended Ising model with short-range interaction. We show that the quantum discord exhibits distinctive behaviors when the system experiences different topological quantum phases denoted by different topological numbers. Quantum discords capability to detect a topological quantum phase transition is more reliable than that of entanglement at both zero and finite temperatures. In addition, by analyzing the divergent behaviors of quantum discord at the critical points, we find that the quantum phase transitions driven by different parameters of the model can also display distinctive critical behaviors, which provides a scheme to detect the topological quantum phase transition in practice.

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References

  1. Sachdev, S.: Quantum Phase Transition. Cambridge University Press, Cambridge (2011)

    Book  MATH  Google Scholar 

  2. Hasan, M.Z., Kane, C.L.: Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010)

    Article  ADS  Google Scholar 

  3. Qi, X.L., Zhang, S.C.: Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011)

    Article  ADS  Google Scholar 

  4. Zhang, G., Song, Z.: Topological characterization of extended quantum Ising models. Phys. Rev. Lett. 115, 177204 (2015)

    Article  ADS  Google Scholar 

  5. Kopp, A., Chakravarty, S.: Criticality in correlated quantum matter. Nat. Phys. 1, 53 (2005)

    Article  Google Scholar 

  6. Quan, H.T., Song, Z., Liu, X.F., Zanardi, P., Sun, C.P.: Decay of loschmidt echo enhanced by quantum criticality. Phys. Rev. Lett. 96, 140604 (2006)

    Article  ADS  Google Scholar 

  7. Zhu, S.L.: Scaling of geometric phases close to the quantum phase transition in the XY spin chain. Phys. Rev. Lett. 96, 077206 (2006)

    Article  ADS  Google Scholar 

  8. Zanardi, P., Quan, H.T., Wang, X.G., Sun, C.P.: Mixed-state fidelity and quantum criticality at finite temperature. Phys. Rev. A 75, 032109 (2007)

    Article  ADS  Google Scholar 

  9. Divakaran, U.: Three-site interacting spin chain in a staggered field: fidelity versus Loschmidt echo. Phys. Rev. E 88, 052122 (2013)

    Article  ADS  Google Scholar 

  10. Dutta, A., Aeppli, G., Chakrabarti, B.K., Divakaran, U., Rosenbaum, T., Sen, D.: Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information. Cambridge University Press, Cambridge (2015)

    Book  MATH  Google Scholar 

  11. Osterloh, A., Amico, L., Falci, G., Fazio, R.: Scaling of entanglement close to a quantum phase transition. Nature 416, 608 (2002)

    Article  ADS  Google Scholar 

  12. Osborne, T.J., Nielsen, M.A.: Entanglement in a simple quantum phase transition. Phys. Rev. A 66, 032110 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  13. Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90, 227902 (2003)

    Article  ADS  Google Scholar 

  14. Gu, S.S., Deng, S.S., Li, Y.Q., Lin, H.Q.: Entanglement and quantum phase transition in the extended Hubbard model. Phys. Rev. Lett. 93, 086402 (2004)

    Article  ADS  Google Scholar 

  15. Wu, L.A., Sarandy, M.S., Lidar, D.A.: Quantum phase transitions and bipartite entanglement. Phys. Rev. Lett. 93, 250404 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  16. Legeza, O., Sólyom, J.: Two-site entropy and quantum phase transitions in low-dimensional models. Phys. Rev. Lett. 96, 116401 (2006)

    Article  ADS  Google Scholar 

  17. Song, S.Q., Gu, J.L.: Local entanglement and quantum phase transition in a one-dimensional transverse field Ising model. Phys. Rev. A 74, 032308 (2006)

    Article  ADS  Google Scholar 

  18. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  MATH  Google Scholar 

  19. Werlang, T., Trippe, C., Ribeiro, G.A.P., Rigolin, G.: Quantum correlations in spin chains at finite temperatures and quantum phase transitions. Phys. Rev. Lett. 105, 095702 (2010)

    Article  ADS  Google Scholar 

  20. Li, Y.C., Lin, H.Q.: Thermal quantum and classical correlations and entanglement in the XY spin model with three-spin interaction. Phys. Rev. A 83, 052323 (2011)

    Article  ADS  Google Scholar 

  21. Liu, B.Q., Shao, B., Li, J.G., Zou, J., Wu, L.A.: Quantum and classical correlations in the one-dimensional XY model with Dzyaloshinskii-Moriya interaction. Phys. Rev. A 83, 052112 (2011)

    Article  ADS  Google Scholar 

  22. Maziero, J., Guzman, H.C., Céleri, L.C., Sarandy, M.S., Serra, R.M.: Quantum and classical thermal correlations in the XY spin-1/2 chain. Phys. Rev. A 82, 012106 (2010)

    Article  ADS  Google Scholar 

  23. Campbell, S., Richens, J., Nicola, L.G., Busch, T.: Criticality, factorization, and long-range correlations in the anisotropic X Y model. Phys. Rev. A 88, 062305 (2013)

    Article  ADS  Google Scholar 

  24. Çakmak, B., Karpat, G., Gedik, Z.: Critical point estimation and long-range behavior in the one-dimensional XY model using thermal quantum and total correlations. Phys. Lett. A 376, 2982 (2012)

    Article  ADS  Google Scholar 

  25. Sarandy, M.S.: Classical correlation and quantum discord in critical systems. Phys. Rev. A 80, 022108 (2009)

    Article  ADS  Google Scholar 

  26. Altintas, F., Eryigit, R.: Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems. Ann. Phys. 327, 3084 (2012)

    Article  ADS  MATH  Google Scholar 

  27. Werlang, T., Ribeiro, G.A.P., Rigolin, G.: Interplay between quantum phase transitions and the behavior of quantum correlations at finite temperatures. Int. J. Mod. Phys. B 27, 1345032 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Guo, J.G., Zhang, X.Z.: Quantum correlation dynamics subjected to critical spin environment with short-range anisotropic interaction. Sci. Rep. 6, 32634 (2016)

    Article  ADS  Google Scholar 

  29. Cai, J.M., Zhou, Z.W., Guo, G.C.: Robustness of entanglement as a signature of quantum phase transitions. Phys. Lett. A 352, 196 (2006)

    Article  ADS  MATH  Google Scholar 

  30. Wang, X., Zanardi, P.: Quantum entanglement and Bell inequalities in Heisenberg spin chains. Phys. Lett. A 301, 1 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Lieb, E., Schultz, T., Mattis, D.: Two soluble models of an antiferromagnetic chain. Ann. Phys. (N.Y.) 16, 407 (1961)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Barouch, E., McCoy, B.M.: Statistical mechanics of the XY model. II. Spin-Correlation functions. Phys. Rev. A 3, 786 (1971)

    Article  ADS  Google Scholar 

  33. Lou, P., Lee, J.Y.: Block-block entanglement and quantum phase transition in the spin-1/2 XX chain. Phys. Rev. B 74, 134402 (2006)

    Article  ADS  Google Scholar 

  34. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  MATH  Google Scholar 

  35. Zhang, G., Li, C., Song, Z.: Majorana charges, winding numbers and Chern numbers in quantum Ising models. arXiv:1606.00420

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Acknowledgements

This work was supported by the National Natural Science Foundation of China Grant Nos. 11305114, and 11505126. X.Z.Z. is also supported by Ph.D. research startup foundation of Tianjin Normal University under Grant No. 52XB1415.

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Authors and Affiliations

  1. College of Physics and Materials Science, Tianjin Normal University, Tianjin, 300387, China

    Xi-Zheng Zhang & Jin-Liang Guo

  2. Tianjin International Joint Research Center of Surface Technology for Energy Storage Materials, Tianjin Normal University, Tianjin, 300387, China

    Xi-Zheng Zhang & Jin-Liang Guo

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  1. Xi-Zheng Zhang
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Correspondence to Jin-Liang Guo.

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Zhang, XZ., Guo, JL. Quantum correlation and quantum phase transition in the one-dimensional extended Ising model. Quantum Inf Process 16, 223 (2017). https://doi.org/10.1007/s11128-017-1670-3

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  • DOI: https://doi.org/10.1007/s11128-017-1670-3

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