Three-Spin System in the Presence of the Quantum Cluster Interaction

  • Z. Noorinezhad
  • B. Haghdoust
  • M. R. Abolhassani
  • M. Ilkhani
  • S. MahdavifarEmail author
Original Paper


We consider a three-spin system under Heisenberg and quantum cluster interactions. Firstly, by focusing on the entanglement between each pair of them at zero temperature, we show that where the quantum phase transition (QPT) of the infinite-size system might happen can be observed even for a such finite spin system. In fact, where the QPT happened, the ground state of the mentioned three-spin system will become the W-state, which is the main reason of possibility of detecting the place of an infinite-size system. Secondly, we investigate the thermal entanglement and show that corresponding to the temperature increase, the mentioned point goes toward the larger exchange coupling constant values, whereas the amount of entanglement decreases, that the latter meets our expectation. Then by using the one-tangle method, we show that at zero temperature, QPT is taken place at the same point. Finally, by using the logarithmic negativity measure, we investigate the role of thermal fluctuations on the previously mentioned finite spin system.


Cluster interaction Three-spin system Entanglement W-state 



  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2000)zbMATHGoogle Scholar
  2. 2.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Rev. Mod. Phys. 81, 865 (2009)CrossRefGoogle Scholar
  3. 3.
    Li, Y., et al.: Chinese Phys. B 27, 020307 (2018)CrossRefGoogle Scholar
  4. 4.
    Golkar, S., Tavassoly, M.K.: Chinese Phys. B 27, 040303 (2018)CrossRefGoogle Scholar
  5. 5.
    Sachdev, S.: Quantum Phase Transitions. Cambridge University Press, New York (2000)CrossRefzbMATHGoogle Scholar
  6. 6.
    O’Connor, K.M., Wootters, W.K.: Phys. Rev. A 63, 052302 (2001)CrossRefGoogle Scholar
  7. 7.
    Kamta, G.L., Starace, A.F.: Phys. Rev. Lett. 88, 107901 (2002)CrossRefGoogle Scholar
  8. 8.
    Osterloh, A., Amico, L., Falci, G., Fazio, R.: Nature 416, 608 (2002)CrossRefGoogle Scholar
  9. 9.
    Osborne, T.J., Nielsen, M.A.: Phys. Rev. A 66, 032110 (2002)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Phys. Rev. Lett. 90, 227902 (2003)CrossRefGoogle Scholar
  11. 11.
    Vidal, J., Palacios, G., Mosseri, R.: Phys. Rev. A 69, 022107 (2004)CrossRefGoogle Scholar
  12. 12.
    Shi-Jian, G., Shu-Sa, D., Hai-Qing, L.: Phys. Rev. B 74, 045103 (2006)CrossRefGoogle Scholar
  13. 13.
    Syljuasen, O.F.: Phys. Rev. A 68, 060301 (2003)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Shi-Jian, G., Shu-Sa, D., Li, Y.-Q., Hai-Qing, L.: Phys. Rev. Lett. 93, 086402 (2004)CrossRefGoogle Scholar
  15. 15.
    Xin, L.I., Zhong-Fang, L.I., Zhi-Long, S.H.I., Xiao-Qin, W.: Chin. Phys. Lett. 31, 060301 (2014)CrossRefGoogle Scholar
  16. 16.
    Wootters, W.K.: Phys. Rev. Lett. 80, 2245 (1998)CrossRefGoogle Scholar
  17. 17.
    Chen, L., Chen, Y.X.: Phys. Rev. A 74, 062310 (2006)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Acin, A., Andrianov, A., Costa, L., Jane, E., Latorre, J.I., Tarrach, R.: Phys. Rev. Lett. 85, 1560 (2000)CrossRefGoogle Scholar
  19. 19.
    Carteret, H.A., Higuchi, A., Sudbery, A.: J. Math. Phys. 41, 7932 (2000)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Acin, A., Bruss, D., Lewenstein, M., Sanpera, A.: Phys. Rev. Lett. 87, 040401 (2001)MathSciNetCrossRefGoogle Scholar
  21. 21.
    de Vicente, J.I., Carle, T., Streitberger, C., Kraus, B.: Phys. Rev. Lett. 108, 060501 (2012)CrossRefGoogle Scholar
  22. 22.
    Vertesi, T., Laskowski, W., Pal, K.F.: Phys. Rev. A 89, 012115 (2014)CrossRefGoogle Scholar
  23. 23.
    Jing, X., Lin, Y., Jin-Lei, W., Xin, J.: Chinese Phys. B 26, 090301 (2017)CrossRefGoogle Scholar
  24. 24.
    Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Nature 464, 45 (2010)CrossRefGoogle Scholar
  25. 25.
    Laflamme, R., Knill, E., Zurek, W.H., Catasti, P., Mariappan, S.V.: Phil. Trans. Roy. Soc. Lond. A 356, 1941 (1998)CrossRefGoogle Scholar
  26. 26.
    Nelson, R.J., Cory, D.G., Lloyd, S.: Phys. Rev. A 61, 022106 (2000)CrossRefGoogle Scholar
  27. 27.
    Mikami, H., Li, Y., Fukuoka, K., Kobayashi, T.: Phys. Rev. Lett. 95, 150404 (2005)CrossRefGoogle Scholar
  28. 28.
    Resch, K.J., Walther, P., Zeilinger, A.: Phys. Rev. Lett. 94, 070402 (2005)CrossRefGoogle Scholar
  29. 29.
    Roos, C.F., Riebe, M., Haffner, H., Hansel, W., Benhelm, J., Lancaster, G.P., Becher, C., Schmidt-Kaler, F., Blatt, R.: Science 304, 1478 (2004)CrossRefGoogle Scholar
  30. 30.
    Shao-Ming, F., Ming-Jing, Z., Kai, C., Zhi-Xi, W.: Phys. Rev. A 80, 032320 (2009)CrossRefGoogle Scholar
  31. 31.
    Mintert, F., Kus, M., Buchleitner, A.: Phys. Rev. Lett. 95, 260502 (2005)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Titvinidze, I., Japaridze, G.I.: Eur. Phys. J. B 32, 383 (2003)CrossRefGoogle Scholar
  33. 33.
    Wang, X.: Phys. Rev. A 64, 012313 (2001)CrossRefGoogle Scholar
  34. 34.
    Dur, W., Vidal, G., Cirac, J.I.: Phys. Rev. A 62, 062314 (2000)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Coffman, V., Kundu, J., Wootters, W.K.: Phys. Rev. A 61, 052306 (2000)CrossRefGoogle Scholar
  36. 36.
    Amico, L., Osterloh, A., Plastina, F., Fazio, R., Palma, G.M.: Phys. Rev. A 69, 022304 (2004)CrossRefGoogle Scholar
  37. 37.
    Eisert, J., Felbinger, T., Papadopoulos, P., Plenio, M.B., Wilkens, M.: Phys. Rev. Lett. 84, 1611 (2000)CrossRefGoogle Scholar
  38. 38.
    Vollbrecht, K.G.H., Werner, R.F.: Phys. Rev. A 64, 062307 (2001)CrossRefGoogle Scholar
  39. 39.
    Bhatia, R.: Matrix analysis. Springer, Heidelberg (1997)CrossRefzbMATHGoogle Scholar
  40. 40.
    Vidal, G., Werner, R.F.: Phys. Rev. A 65, 032314 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Physics, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Department of PhysicsUniversity of GuilanRashtIran
  3. 3.Department of PhysicsIslamic Azad UniversityTehranIran

Personalised recommendations