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New insights into quantum and classical correlations in XY spin models

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Abstract

We compute quantum dissonance Q (non-entangled quantum correlation), entanglement E, quantum discord D (total quantum correlation) and classical correlation C for spin pairs at any distance in the infinite XY spin-1/2 chains, i.e., the anisotropic XY model and the isotropic XY model with three-spin interactions. We obtain two simple dominance relations: C ≥ E and D ≥ E + Q Except this, there are no other simple ordering relations between them. We also show that Q can detect the special points of the system where the entanglement just appears or completely disappears. In addition, it is worthwhile to mention that dissonance and classical correlation can also clearly spotlight the critical points of quantum phase transitions in XY spin-1/2 chains.

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References

  1. C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. C.H. Bennett, G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing (IEEE press, Bangalore, 1984)

  3. C.H. Bennett, D.P. DiVincenzo, Nature 404, 247 (2000)

    Article  ADS  Google Scholar 

  4. A. Datta, S.T. Flammia, C.M. Caves, Phys. Rev. A 72, 042316 (2005)

    Article  ADS  Google Scholar 

  5. A. Datta, G. Vidal, Phys. Rev. A 75, 042310 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  6. A. Datta, A. Shaji, C.M. Caves, Phys. Rev. Lett. 100, 050502 (2008)

    Article  ADS  Google Scholar 

  7. B.P. Lanyon, M. Barbieri, M.P. Almeida, A.G. White, Phys. Rev. Lett. 101, 200501 (2008)

    Article  ADS  Google Scholar 

  8. H. Ollivier, W.H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  Google Scholar 

  9. L. Henderson, V. Vedral, J. Phys. A 34, 6899 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. J. Oppenheim, M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 89, 180402 (2002)

    Article  ADS  Google Scholar 

  11. B. Groisman, S. Popescu, A. Winter, Phys. Rev. 72, 032317 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  12. D. Girolami, G. Adesso, Phys. Rev. A 83, 052108 (2011)

    Article  ADS  Google Scholar 

  13. M. Ali, A.R.P. Rau, G. Alber, Phys. Rev. A 81, 042105 (2010)

    Article  ADS  Google Scholar 

  14. S. Luo, Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  15. J. Maziero, H.C. Guzman, L.C. Céleri, M.S. Sarandy, R.M. Serra, Phys. Rev. A 82, 012106 (2010)

    Article  ADS  Google Scholar 

  16. T. Werlang, C. Trippe, G.A.P. Ribeiro, G. Rigolin, Phys. Rev. Lett. 105, 095702 (2010)

    Article  ADS  Google Scholar 

  17. M.S. Sarandy, Phys. Rev. A 80, 022108 (2009)

    Article  ADS  Google Scholar 

  18. J. Maziero, L.C. Céleri, R.M. Serra, V. Vedral, Phys. Rev. A 80, 044102 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  19. Y.-X. Chen, S.-W. Li, Phys. Rev. A 81, 032120 (2010)

    Article  ADS  Google Scholar 

  20. T. Werlang, G.A.P. Ribeiro, G. Rigolin, Phys. Rev. A 83, 062334 (2011)

    Article  ADS  Google Scholar 

  21. Y.-C. Li, H.-Q. Lin, Phys. Rev. A 83, 052323 (2011)

    Article  ADS  Google Scholar 

  22. J. Maziero, L. Céleri, R. Serra, M. Sarandy, Phys. Lett. A 376, 1540 (2010)

    Article  ADS  Google Scholar 

  23. K. Modi, T. Paterek, W. Son, V. Vedral, M. Williamson, Phys. Rev. Lett. 104, 080501 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  24. V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, Phys. Rev. Lett. 78, 2275 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. L. Ciliberti, R. Rossignoli, N. Canosa, Phys. Rev. A 82, 042316 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  26. N. Li, S. Luo, Phys. Rev. A 76, 032327 (2007)

    Article  ADS  Google Scholar 

  27. J.-S. Xu et al., Nat. Communication. 1, 7 (2010)

    ADS  Google Scholar 

  28. G. Lindblad, Lecture Notes in Physics (Springer, Berlin, 1991), Vol. 378, p. 71

  29. S. Sachdev, Quantum phase transitions, 2nd edn (Cambridge University Press, Cambridge, 2011)

  30. V. Vedral, M.B. Plenio, Phys. Rev. A 57, 1619 (1998)

    Article  ADS  Google Scholar 

  31. E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 16, 407 (1961)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. E. Barouch, B.M. McCoy, M. Dresden, Phys. Rev. A 2, 1075 (1970)

    Article  ADS  Google Scholar 

  33. E. Barouch, B.M. McCoy, Phys. Rev. A 3, 786 (1971)

    Article  ADS  Google Scholar 

  34. P. Lou, W.-C. Wu, M.-C. Chang, Phys. Rev. B 70, 064405 (2004)

    Article  ADS  Google Scholar 

  35. I. Titvinidze, G.I. Japaridze, Eur. Phys. J. B 32, 383 (2003)

    Article  ADS  Google Scholar 

  36. P. Lou, J.-Y. Lee, Phys. Rev. B 74, 134402 (2006)

    Article  ADS  Google Scholar 

  37. O. Derzhko, T. Krokhmalskii, J. Stolze, T. Verkholyak, Phys. Rev. B 79, 094410 (2009)

    Article  ADS  Google Scholar 

  38. M. Topilko et al., arXiv:1205.0727[cond-mat.str-el] (2012)

  39. H. Frahm, J. Phys. A 25, 1417 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  40. C. D’Cruz, J.K. Pachos, Phys. Rev. A 72, 043608 (2005)

    Article  ADS  Google Scholar 

  41. M.-F. Yang, Phys. Rev. A 71, 030302(R) (2005)

    ADS  Google Scholar 

  42. J.K. Pachos, M.B. Plenio, Phys. Rev. Lett. 93, 056402 (2004)

    Article  ADS  Google Scholar 

  43. C.H. Tseng et al., Phys. Rev. A 61, 012302 (1999)

    Article  ADS  Google Scholar 

  44. M.D. Lang, C.M. Caves, Phys. Rev. Lett. 105, 150501 (2010)

    Article  ADS  Google Scholar 

  45. R.F. Werner, Phys. Rev. A 40, 4277 (1989)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou, 325035, P.R. China

    X.D. Tan, S.S. Huang & B.Q. Jin

Authors
  1. X.D. Tan
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  2. S.S. Huang
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  3. B.Q. Jin
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Correspondence to B.Q. Jin.

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Tan, X., Huang, S. & Jin, B. New insights into quantum and classical correlations in XY spin models. Eur. Phys. J. B 85, 411 (2012). https://doi.org/10.1140/epjb/e2012-30641-9

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