Quantum Fisher information and coherence in one-dimensional XY spin models with Dzyaloshinsky-Moriya interactions

  • Biao-Liang YeEmail author
  • Bo Li
  • Zhi-Xi Wang
  • Xianqing Li-Jost
  • Shao-Ming FeiEmail author
Open Access


We investigate quantum phase transitions in XY spin models using Dzyaloshinsky-Moriya (DM) interactions. We identify the quantum critical points via quantum Fisher information and quantum coherence, finding that higher DM couplings suppress quantum phase transitions. However, quantum coherence (characterized by the l1-norm and relative entropy) decreases as the DM coupling increases. Herein, we present both analytical and numerical results.


quantum Fisher information quantum coherence XY spin models Dzyaloshinsky-Moriya interactions 


This work was supported by the National Natural Science Foundation of China (Grant Nos. 11675113, and 11765016), the Natural Science Foundation of Beijing (Grant No. KZ201810028042), and Jiangxi Education Department Fund (Grant Nos. GJJ161056, and KJLD14088). Open access funding provided by Max Planck Society.


  1. 1.
    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).ADSCrossRefGoogle Scholar
  2. 2.
    A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    G. L. Long, and X. S. Liu, Phys. Rev. A 65, 032302 (2002).ADSCrossRefGoogle Scholar
  4. 4.
    F. G. Deng, G. L. Long, and X. S. Liu, Phys. Rev. A 68, 042317 (2003).ADSCrossRefGoogle Scholar
  5. 5.
    W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B. S. Shi, and G. C. Guo, Phys. Rev. Lett. 118, 220501 (2017), arXiv: 1609.09184.ADSCrossRefGoogle Scholar
  6. 6.
    F. Zhu, W. Zhang, Y. Sheng, and Y. Huang, Sci. Bull. 62, 1519 (2017).CrossRefGoogle Scholar
  7. 7.
    F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, Sci. China-Phys. Mech. Astron. 60, 120313 (2017).ADSCrossRefGoogle Scholar
  8. 8.
    Y. B. Sheng, and L. Zhou, Sci. Bull. 62, 1025 (2017).CrossRefGoogle Scholar
  9. 9.
    C. M. Xie, Y. M. Liu, J. L. Chen, X. F. Yin, and Z. J. Zhang, Sci. China-Phys. Mech. Astron. 59, 100314 (2016).CrossRefGoogle Scholar
  10. 10.
    A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature 416, 608 (2002).ADSCrossRefGoogle Scholar
  11. 11.
    T. J. Osborne, and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002).ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003).ADSCrossRefGoogle Scholar
  13. 13.
    H. Ollivier, and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001).ADSCrossRefGoogle Scholar
  14. 14.
    L. Henderson, and V. Vedral, J. Phys. A-Math. Gen. 34, 6899 (2001).ADSCrossRefGoogle Scholar
  15. 15.
    J. Oppenheim, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 89, 180402 (2002).ADSCrossRefGoogle Scholar
  16. 16.
    S. Luo, Phys. Rev. A 77, 022301 (2008).ADSCrossRefGoogle Scholar
  17. 17.
    K. Modi, T. Paterek, W. Son, V. Vedral, and M. Williamson, Phys. Rev. Lett. 104, 080501 (2010), arXiv: 0911.5417.ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012), arXiv: 1112.6238.ADSCrossRefGoogle Scholar
  19. 19.
    G. Adesso, T. R. Bromley, and M. Cianciaruso, J. Phys. A-Math. Theor. 49, 473001 (2016), arXiv: 1605.00806.ADSCrossRefGoogle Scholar
  20. 20.
    B. Q. Liu, B. Shao, J. G. Li, J. Zou, and L. A. Wu, Phys. Rev. A 83, 052112 (2011), arXiv: 1012.2788.ADSCrossRefGoogle Scholar
  21. 21.
    R. Dillenschneider, Phys. Rev. B 78, 224413 (2008), arXiv: 0809.1723.ADSCrossRefGoogle Scholar
  22. 22.
    M. S. Sarandy, Phys. Rev. A 80, 022108 (2009), arXiv: 0905.1347.ADSCrossRefGoogle Scholar
  23. 23.
    T. Werlang, C. Trippe, G. A. P. Ribeiro, and G. Rigolin, Phys. Rev. Lett. 105, 095702 (2010), arXiv: 1006.3332.ADSCrossRefGoogle Scholar
  24. 24.
    S. Campbell, J. Richens, N. L. Gullo, and T. Busch, Phys. Rev. A 88, 062305 (2013), arXiv: 1309.1052.ADSCrossRefGoogle Scholar
  25. 25.
    J. D. Montealegre, F. M. Paula, A. Saguia, and M. S. Sarandy, Phys. Rev. A 87, 042115 (2013), arXiv: 1303.5110.ADSCrossRefGoogle Scholar
  26. 26.
    B. L. Ye, B. Li, L. J. Zhao, H. J. Zhang, and S. M. Fei, Sci. China-Phys. Mech. Astron. 60, 030311 (2017), arXiv: 1702.03123.ADSCrossRefGoogle Scholar
  27. 27.
    G. Karpat, B. Çakmak, and F. F. Fanchini, Phys. Rev. B 90, 104431 (2014), arXiv: 1404.6427.ADSCrossRefGoogle Scholar
  28. 28.
    A. Misra, A. Biswas, A. K. Pati, A. Sen(De), and U. Sen, Phys. Rev. E 91, 052125 (2015), arXiv: 1406.5065.ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Ł. Czekaj, A. Przysiȩżna, M. Horodecki, and P. Horodecki, Phys. Rev. A 92, 062303 (2015), arXiv: 1403.5867.ADSCrossRefGoogle Scholar
  30. 30.
    Y. C. Li, and H. Q. Lin, Sci. Rep. 6, 26365 (2016).ADSCrossRefGoogle Scholar
  31. 31.
    A. L. Malvezzi, G. Karpat, B. Çakmak, F. F. Fanchini, T. Debarba, and R. O. Vianna, Phys. Rev. B 93, 184428 (2016), arXiv: 1602.03731.ADSCrossRefGoogle Scholar
  32. 32.
    C. Radhakrishnan, I. Ermakov, and T. Byrnes, Phys. Rev. A 96, 012341 (2017), arXiv: 1707.03545.ADSCrossRefGoogle Scholar
  33. 33.
    T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014), arXiv: 1311.0275.ADSCrossRefGoogle Scholar
  34. 34.
    S. L. Braunstein, and C. M. Caves, Phys. Rev. Lett. 72, 3439 (1994).ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. Lett. 96, 010401 (2006).ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    X. M. Liu, W. W. Cheng, and J. M. Liu, Sci. Rep. 6, 19359 (2016).ADSCrossRefGoogle Scholar
  37. 37.
    F. Altintas, and R. Eryigit, Ann. Phys. 327, 3084 (2012), arXiv: 1202.1495.ADSCrossRefGoogle Scholar
  38. 38.
    C.W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976).zbMATHGoogle Scholar
  39. 39.
    A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).zbMATHGoogle Scholar
  40. 40.
    A. Streltsov, G. Adesso, and M. B. Plenio, Rev. Mod. Phys. 89, 041003 (2017), arXiv: 1609.02439.ADSCrossRefGoogle Scholar
  41. 41.
    E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. 16, 407 (1961).ADSCrossRefGoogle Scholar
  42. 42.
    J. H. H. Perk, and H. W. Capel, Physica A 89, 265 (1977).ADSCrossRefGoogle Scholar
  43. 43.
    T. Giamarchi, Quantum Physics in One Dimension (Oxford University, New York, 2004)zbMATHGoogle Scholar
  44. 44.
    N. Li, and S. Luo, Phys. Rev. A 88, 014301 (2013).ADSCrossRefGoogle Scholar

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© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Authors and Affiliations

  1. 1.Quantum Information Research Center, School of Physics and Electronic InformationShangrao Normal UniversityShangraoChina
  2. 2.Jiangxi Province Key Laboratory of Polymer Preparation and ProcessingShangraoChina
  3. 3.School of Mathematics and Computer SciencesShangrao Normal UniversityShangraoChina
  4. 4.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany
  5. 5.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  6. 6.School of Mathematics and StatisticsHainan Normal UniversityHaikouChina

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