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Quantum Correlation Properties in Composite Parity-Conserved Matrix Product States

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Abstract

We give a new thought for constructing long-range quantum correlation in quantum many-body systems. Our proposed composite parity-conserved matrix product state has long-range quantum correlation only for two spin blocks where their spin-block length larger than 1 compared to any subsystem only having short-range quantum correlation, and we investigate quantum correlation properties of two spin blocks varying with environment parameter and spacing spin number. We also find that the geometry quantum discords of two nearest-neighbor spin blocks and two next-nearest-neighbor spin blocks become smaller and for other conditions the geometry quantum discord becomes larger than that in any subcomponent, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation compared to the corresponding classical correlation and total correlation having no any characteristic of regulation. For nearest-neighbor and next-nearest-neighbor all the correlations take their maximal values at the same points, while for other conditions no whether for spacing same spin number or for different spacing spin numbers all the correlations taking their maximal values are respectively at different points which are very close. We believe that our work is helpful to comprehensively and deeply understand the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems; and further helpful for the classification, the depiction and the measure of quantum correlation of quantum many-body systems.

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References

  1. Haldane, FDM.: Phys. Rev. B 25, 4925 (1982)

    Article  ADS  Google Scholar 

  2. Haldane, FDM.: Phys. Lett. A 93, 464 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  3. Haldane, F.D.M.: Phys. Rev. Lett 50, 1153 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  4. Imamoglu, A., Awschalom, D.D., Burkard, G., et al.: Phys. Rev. Lett. 83(20), 4204 (1999)

    Article  ADS  Google Scholar 

  5. Zheng, S.B., Guo, GC.: Phys. Rev. Lett 85(11), 2392 (2000)

    Article  ADS  Google Scholar 

  6. Christandl, M., Datta, N., Ekert, A., et al.: Phys. Rev. Lett. 92(18), 187902 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  7. Vestraete, F., Martin-Delgado, M.A., Cirac, JI.: Phys. Rev. Lett 92, 087201 (2004)

    Article  ADS  Google Scholar 

  8. Grigorenko, I.A., Khveshchenko, D.V.: Phys. Rev. Lett. 95(8), 110501 (2005)

    Article  ADS  Google Scholar 

  9. Fan, H., Roychowdhury, V., Szkopek, T.: Phys. Rev. A 72(11), 052323 (2005)

    Article  ADS  Google Scholar 

  10. Barjaktarevic, J.P., McKenzie, R.H., Links, J., et al.: Phys. Rev. Lett. 95(12), 230501 (2005)

    Article  ADS  Google Scholar 

  11. Murao, M., Jonathan, D., Plenio, M.B., et al.: Phys. Rev. A 59(1), 156 (1999)

    Article  ADS  Google Scholar 

  12. Affleck, I., Kennedy, T., Lieb, E.H., Tasaki, H.: Commun. Math. Phys 115, 477 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  13. Klümper, A., Schadschneider, A., Zittartz, J.: J. Phys. A 24, L955 (1991)

    Article  ADS  Google Scholar 

  14. Klümper, A., Schadschneider, A., Zittartz, J.: Z. Phys. B 87, 281 (1992)

    Article  ADS  Google Scholar 

  15. Fannes, M., Nachtergaele, B., Werner, R.F.: Commun. Math. Phys 144, 443 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  16. Verstraete, F., Porras, D., Cirac, J.I.: Phys. Rev. Lett 93, 227205 (2004)

    Article  ADS  Google Scholar 

  17. Verstraete, F., Garcia-Ripoll, J.J., Cirac, J.I.: Phys. Rev. Lett 93, 207204 (2004)

    Article  ADS  Google Scholar 

  18. Verstraete, F., Cirac, J.I.: arXiv:cond-mat/0505140

  19. Osborne, T.J.: arXiv:quant-ph/0508031

  20. Hastings, M.B.: arXiv:cond-mat/0508554

  21. Zwolak, M., Vidal, G.: Phys. Rev. Lett 93, 207205 (2004)

    Article  ADS  Google Scholar 

  22. Vidal, G.: Phys. Rev. Lett 93, 040502 (2004)

    Article  ADS  Google Scholar 

  23. Garcia, D.P., Verstraete, F., Wolf, M.M., Cirac, J.I.: Quantum Inf. Comput 7, 401 (2007)

    MathSciNet  Google Scholar 

  24. Zhu, J.M.: Int. J. Mod. Phys. B 29, 1550071 (2015)

    Article  ADS  Google Scholar 

  25. Asoudeh, M., Karimipour, V., Sadrelashrafi, A.: Phys. Rev. B 75, 224427 (2007)

    Article  ADS  Google Scholar 

  26. Alipour, S., Karimipour, V., Memarzadeh, L.: Phys. Rev. A 75, 052322 (2007)

    Article  ADS  Google Scholar 

  27. Cozzini, M., Ionicioiu, R., Zanardi, P.: Phys. Rev. B 76, 104420 (2007)

    Article  ADS  Google Scholar 

  28. Zhu, J.M.: Chin. Phys. Lett 25, 3574 (2008)

    Article  ADS  Google Scholar 

  29. Zhu, J.M.: Commun. Theor. Phys 54(2), 373–379 (2010)

    Article  ADS  Google Scholar 

  30. Zhu, J.M.: Chin. Phys. C 36(4), 294–298 (2012)

    Article  Google Scholar 

  31. Zhu, J.M.: Commun. Theor. Phys 64(3), 356–360 (2015)

    Article  ADS  Google Scholar 

  32. Feng, Z.G.: Physics 42(8), 552–557 (2013)

    Google Scholar 

  33. Ma, X.S., Ying, Q., et al: Sci. China Phy. Mech. Astronom. 56(3), 600–605 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  34. Tao, Z., Long, G.L., et al: Physics 42(8), 544–551 (2013)

    Google Scholar 

  35. Wei, W.: Sci. China Phy. Mech. Astronom. 56(5), 947–951 (2013)

    Article  ADS  Google Scholar 

  36. Yao, Y., Li, H.W., et al: Phy. Rev. A 86, 042102 (2012)

    Article  ADS  Google Scholar 

  37. Hui, Z., Hua, Z.X., Ming, F.S., et al: Chin. Sci. Bull 58(19), 2334–2339 (2013)

    Article  Google Scholar 

  38. Xiao, M.Z., Fang, S., Jie, X.Y.: Chin. Sci. Bull 58(20), 2423–2429 (2013)

    Article  Google Scholar 

  39. Cang, C.W., Dan, L., Feng, P., et al: Sci. China Ser. G-Phy. Mech. Astronom 49(5), 606 (2006)

    Article  ADS  Google Scholar 

  40. Liu, D., Zhao, X., Long, G.L.: Commun. Theor. Phys 54, 825 (2010)

    Article  ADS  Google Scholar 

  41. Liu, D., Zhao, X., Long, G.L.: Commun. Theor. Phys 49, 329 (2008)

    Article  ADS  Google Scholar 

  42. Wu, H., Zhao, X., Li, Y.S.: Int. J. Quantum Inform 8, 1169 (2010)

    Article  Google Scholar 

  43. Muralidharan, S., Panigrahi, P.K.: Phy. Rev. A 77, 032321 (2008)

    Article  ADS  Google Scholar 

  44. Muralidharan, S., Panigrahi, P.K.: Phy. Rev. A 78, 062333 (2008)

    Article  ADS  Google Scholar 

  45. Zhu, J.M.: Chin. Phys. C 36, 311 (2012)

    Article  ADS  Google Scholar 

  46. Ye, C., Li, H., Long Gui, L.: Chin. Sci. Bull 58(1), 48–52 (2013)

    Article  Google Scholar 

  47. Dakié, B., Vedral, V., Brukner, C.: Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No.10974137 and the Major Natural Science Foundation of the Educational Department of Sichuan Province under Grant No.14ZA0167.

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  1. College of Optoelectronics Technology, Chengdu University of Information Technology, Chengdu, 610225, China

    Jing-Min Zhu

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  1. Jing-Min Zhu
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Correspondence to Jing-Min Zhu.

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Zhu, JM. Quantum Correlation Properties in Composite Parity-Conserved Matrix Product States. Int J Theor Phys 55, 4157–4175 (2016). https://doi.org/10.1007/s10773-016-3042-7

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  • DOI: https://doi.org/10.1007/s10773-016-3042-7

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