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Journal of Low Temperature Physics

, Volume 186, Issue 3–4, pp 217–232 | Cite as

Zero-Temperature Study of a Tetrameric Spin-1/2 Chain in a Transverse Magnetic Field

  • J. VahediEmail author
  • M. Shabani Arbousara
  • S. Mahdavifar
Article

Abstract

We consider an alternating Heisenberg spin-1/2 antiferromagnetic–ferromagnetic chain with the space-modulated dominant antiferromagnetic exchange and anisotropic ferromagnetic coupling (tetrameric spin-1/2 chain). The zero-temperature effect of a symmetry breaking transverse magnetic field on the model is studied numerically. It is found that the anisotropy effect on the ferromagnetic coupling induces two new gapped phases. We identified their orderings as a kind of the stripe antiferromagnetic phase. As a result, the magnetic phase diagram of the tetrameric chain shows five gapped quantum phases, and the system is characterized by four critical fields which mark quantum phase transitions in the ground state of the system with the changing transverse magnetic field. We have also exploited the well-known bipartite entanglement (name as concurrence) and global entanglement tools to verify the occurrence of quantum phase transitions and the corresponding critical points.

Keywords

Spin-1/2 chain Alternating Heisenberg spin-1/2 Transverse magnetic field 

References

  1. 1.
    S. Sachdev, Quantum Phase transitions. Cambridge University Press. ISBN 0-521-00454-3 (2001)Google Scholar
  2. 2.
    S. Takada, J. Phys. Soc. Jpn. 61, 428 (1992)ADSCrossRefGoogle Scholar
  3. 3.
    K. Hida, S. Takada, J. Phys. Soc. Jpn. 61, 1879 (1992)ADSCrossRefGoogle Scholar
  4. 4.
    K. Hida, Phys. Rev. B 46, 8268 (1992)ADSCrossRefGoogle Scholar
  5. 5.
    K. Hida, Phys. Rev. B 45, 2207 (1992)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    K. Hida, J. Phys. Soc. Jpn. 62, 439 (1993)ADSCrossRefGoogle Scholar
  7. 7.
    K. Hida, J. Phys. Soc. Jpn. 63, 2514 (1994)ADSCrossRefGoogle Scholar
  8. 8.
    M. Kohmoto, H. Tasaki, Phys. Rev. B 46, 3486 (1992)ADSCrossRefGoogle Scholar
  9. 9.
    M. Yamanaka, Y. Hatsugai, M. Kohmoto, Phys. Rev. B 48, 9555 (1993)ADSCrossRefGoogle Scholar
  10. 10.
    T. Sakai, J. Phys. Soc. Jpn. 64, 251 (1995)ADSCrossRefGoogle Scholar
  11. 11.
    G.S. Uhrig, H.J. Schulz, Phys. Rev. B 54, R9624 (1996)ADSCrossRefGoogle Scholar
  12. 12.
    T. Barnes, J. Riera, D.A. Tennant, Phys. Rev. B 59, 11384 (1999)ADSCrossRefGoogle Scholar
  13. 13.
    M. Bocquet, T. Jolicoeur, Eur. Phys. J. B 14, 47 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    S. Yamamoto, K. Funase, Low Temp. Phys. 31, 740 (2005)ADSCrossRefGoogle Scholar
  15. 15.
    W. Zheng, C.J. Hamer, R.R.P. Singh, Phys. Rev. B 74, 172407 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    S. Mahdavifar, A. Akbari, J. Phys. Soc. Jpn. 77, 024710 (2008)ADSCrossRefGoogle Scholar
  17. 17.
    J. Abouie, S. Mahdavifar, Phys. Rev. B 78, 184437 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    G.Q. Zhong, S.S. Gong, Q.R. Zheng, G. Su, Phys. Lett. A 373, 1687 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    M. Schmitt, O. Janson, S. Golbs, M. Schmidt, W. Schnelle, J. Richter, H. Rosner, Phys. Rev. B 89, 174403 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    G.H. Liu, W. Li, G. Su, G.S. Tian, Eur. Phys. J. B 87, 105 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    B. Willenberg, H. Ryll, K. Kiefer, D.A. Tennant, F. Groitl, K. Rolfs, P. Manuel, D. Khalyavin, K.C. Rule, A.U.B. Wolter, S. Süllow, Phys. Rev. B 91, 060407(R) (2015)ADSCrossRefGoogle Scholar
  22. 22.
    Y.-C. Tzeng, L. Dai, M.-C. Chung, L. Amico, L.-C. Kwek, Sci. Rep. 6, 26453 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    M. Hagiwara, Y. Narumi, K. Kindo, T.C. Kobayashi, H. Yamakage, K. Amaya, G. Schumauch, J. Phys. Soc. Jpn. 66, 1792 (1997)ADSCrossRefGoogle Scholar
  24. 24.
    M. Takahashi, Y. Hosokoshi, H. Nakano, T. Goto, M. Kinoshita, Mol. Cryst. Liq. Crist. Sci. Technol. Sec. A 306, 111 (1997)CrossRefGoogle Scholar
  25. 25.
    B. Lake, R.A. Cowley, D.A. Tennant, J. Phys. Condens. Matter 9, 10951 (2000)ADSCrossRefGoogle Scholar
  26. 26.
    A.W. Garrett, S.E. Nagler, D.A. Tennant, B.C. Sales, T. Barnes, Phys. Rev. Lett. 79, 745 (1997)ADSCrossRefGoogle Scholar
  27. 27.
    H. Manaka, I. Yamada, K. Yamaguchi, J. Phys. Soc. Jpn. 66, 564 (1997)ADSCrossRefGoogle Scholar
  28. 28.
    H. Manaka, I. Yamada, J. Phys. Soc. Jpn. 66, 1908 (1997)ADSCrossRefGoogle Scholar
  29. 29.
    K. Kodama, H. Harashina, H. Sakai, M. Kato, M. Sato, K. Kakurai, M. Nishi, J. Phys. Soc. Jpn. 68, 237 (1999)ADSCrossRefGoogle Scholar
  30. 30.
    G. Xu, C. Broholm, D.H. Reich, M.A. Adams, Phys. Rev. Lett. 84, 4465 (2000)ADSCrossRefGoogle Scholar
  31. 31.
    Y. Inagaki, A. Kobayashi, T. Asano, T. Sakon, H. Kitagawa, M. Motokawa, Y. Ajiro, J. Phys. Soc. Jpn. 74, 2683 (2005)ADSCrossRefGoogle Scholar
  32. 32.
    M.B. Stone, W. Tian, M.D. Lumsden, G.E. Granroth, D. Mandrus, J.H. Chung, N. Harrison, S.E. Nagler, Phys. Rev. Lett. 99, 087204 (2007)ADSCrossRefGoogle Scholar
  33. 33.
    M.B. Stone, Y. Chen, D.H. Reich, C. Broholm, G. Xu, J.R.D. Copley, J.C. Cook, Phys. Rev. B 90, 094419 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    H. Yamaguchi, Y. Shinpuku, T. Shimokawa, K. Iwase, T. Ono, Y. Kono, S. Kittaka, T. Sakakibara, Y. Hosokoshi, Phys. Rev. B 91, 085117 (2015)ADSCrossRefGoogle Scholar
  35. 35.
    Y. Ajiro, T. Asano, T. Inami, H. Aruga-Katori, T. Goto, J. Phys. Soc. Jpn. 63, 859 (1994)ADSCrossRefGoogle Scholar
  36. 36.
    K. Hida, J. Phys. Soc. Jpn. 63, 2359 (1994)ADSCrossRefGoogle Scholar
  37. 37.
    K. Okamoto, Solid State Commun. 98, 245 (1996)ADSCrossRefGoogle Scholar
  38. 38.
    A. Escuer, R. Vicente, M.S. El Fallah, M.A.S. Goher, F.A. Mautner, Inorg. Chem. 37, 4466 (1998)CrossRefGoogle Scholar
  39. 39.
    H.T. Lu, Y.H. Su, L.Q. Sun, J. Chang, C.S. Liu, H.G. Luo, T. Iang, Phys. Rev. B 71, 144426 (2005)ADSCrossRefGoogle Scholar
  40. 40.
    Gu Bo, G. Su, S. Gao, Phys. Rev. B 73, 134427 (2006)ADSCrossRefGoogle Scholar
  41. 41.
    S.S. Gong, B. Gu, G. Su, Phys. Lett. A 372, 2322 (2008)ADSCrossRefGoogle Scholar
  42. 42.
    S.S. Gong, G. Song, G. Su, Phys. Rev. B 80, 014413 (2009)ADSCrossRefGoogle Scholar
  43. 43.
    S. Mahdavifar, J. Abouie, J. Phys. Condens. Matter 23, 246002 (2011)ADSCrossRefGoogle Scholar
  44. 44.
    M. Shahri Naseri, G.I. Japaridze, S. Mahdavifar, S. Farjami Shayesteh, J. Phys. Condens. Matter 24, 116002 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    M. Shahri Naseri, G.I. Japaridze, S. Mahdavifar, S. Farjami Shayesteh, Phys. Status Solidi (B) 250, 338 (2012)CrossRefGoogle Scholar
  46. 46.
    Z.K. Cheng, G.S. Tian, C. Feng, Commun. Theor. Phys. 61, 263 (2013)Google Scholar
  47. 47.
    K. Hida, J. Phys. Soc. Jpn. 85, 024705 (2016)ADSCrossRefGoogle Scholar
  48. 48.
    F. Mila, Eur. Phys. J. B 6, 201 (1998)ADSCrossRefGoogle Scholar
  49. 49.
    F.C. Alcaraz, A.L. Malvezzi, J. Phys. A Math. Gen. 28, 1521 (1995)ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    J. Lou et al., Phys. Rev. Lett. 94, 217207 (2005)ADSCrossRefGoogle Scholar
  51. 51.
    S. Mahdavifar, Eur. Phys. J. B 55, 371 (2007)ADSCrossRefGoogle Scholar
  52. 52.
    H. Moradmard, M. Shahri Naseri, S. Mahdavifar, J. Supercond. Nov. Magn. 27, 1265 (2014)CrossRefGoogle Scholar
  53. 53.
    F.D.M. Haldane, Phys. Rev. Lett. 50, 1153 (1983)ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    K. Hida, Phys. Rev. Lett. 83, 3297 (1999)ADSCrossRefGoogle Scholar
  55. 55.
    W.K. Wooters, Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar
  56. 56.
    T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416, 608 (2002)ADSCrossRefGoogle Scholar
  58. 58.
    G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)ADSCrossRefGoogle Scholar
  59. 59.
    P. Lou, J.Y. Lee, Phys. Rev. B 74, 134402 (2006)ADSCrossRefGoogle Scholar
  60. 60.
    L. Amico, R. Fazio, A. Osterloh, V. Vedal, Rev. Mod. Phys. 80, 517 (2008)ADSCrossRefGoogle Scholar
  61. 61.
    D.A. Meyer, N.R. Wallach, J. Math. Phys. 43, 4273 (2002)ADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    G.K. Brennen, Quantum Inf. Comput. 3, 616 (2003)MathSciNetGoogle Scholar
  63. 63.
    J. Vahedi, M.R. Soltani, S. Mahdavifar, J. Supercond. Nov. Magn. 25, 1159 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Physics, Sari BranchIslamic Azad UniversitySariIran
  2. 2.Center for Theoretical Physics of Complex SystemsInstitute for Basic Science (IBS)DaejeonKorea
  3. 3.Department of PhysicsUniversity of GuilanRashtIran

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