Advertisement

Influence of Dzyaloshinskii-Moriya interaction and external fields on quantum entanglement in half-integer spin one-dimensional antiferromagnets

  • Leonardo S. LimaEmail author
Regular Article
  • 15 Downloads

Abstract

The effect of uniform Dzyaloshinskii-Moriya interaction (antisymmetric spin coupling) and arbitrary oriented external magnetic fields in the x̂ and ẑ directions hx, hy, on quantum entanglement is investigated in the quantum spin-1/2 one-dimensional Heisenberg antiferromagnetic model. The Von Neumann entropy of quantum entanglement is calculated employing Abelian bosonization and density matrix renormalization group. We investigate the influence of quantum phase transition of three competing phases (Néel phase, dimerized phase and gapless Luttinger liquid phase) on quantum entanglement at zero-temperature.

Graphical abstract

Keywords

Quantum Information 

References

  1. 1.
    E. Mehran, S. Mahdavifar, R. Jafari, Phys. Rev. A 89, 042306 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    J.-Q. Cheng, W. Wu, J.-B. Xu, Quantum Inf. Process. 16, 231 (2017)ADSCrossRefGoogle Scholar
  3. 3.
    L.S. Lima, Eur. Phys. J. D 73, 6 (2019)ADSCrossRefGoogle Scholar
  4. 4.
    B.-Q. Liu, B. Shao, J.-G. Li, J. Zou, L.-A. Wu, Phys. Rev. A 83, 052112 (2011)ADSCrossRefGoogle Scholar
  5. 5.
    M. Kargarian, R. Jafari, A. Langari, Phys. Rev. A 79, 042319 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    D.-C. Li, Z.-L. Cao, Int. J. Quantum Inf. 07, 547 (2009)CrossRefGoogle Scholar
  7. 7.
    D.-C. Li, X.-P. Wang, Z.-L. Cao, J. Phys. Condens. Matter 20, 325229 (2008)CrossRefGoogle Scholar
  8. 8.
    D.-C. Li, X.-P. Wang, H. Li, X.-M. Li, M. Yang, Z.-L. Gao, Chin. Phys. Lett. 33, 5 (2016)Google Scholar
  9. 9.
    X. Wang, H. Fu, A.I. Solomon, J. Phys. A.: Math. General 50, 11307 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Yeo, T. Liu, Y.-E. Lu, Q.-Z. Yang, J. Phys. A.: Math. General 38, 3235 (2005)CrossRefGoogle Scholar
  11. 11.
    E. Albayrak, Eur. Phys. J. B 72, 491 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    A. Abliz, J.-T. Cai, G.-F. Zhang, G.-S. Jin, J. Phys. B: At. Mol. Opt. Phys. 42, 215503 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    S. Mahdavifar, S. Mahdavifar, R. Jafari, Phys. Rev. A 96, 052303 (2017)ADSCrossRefGoogle Scholar
  14. 14.
    E. Mehran, S. Mahdavifar, R. Jafari, Phys. Rev. A 89, 042306 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    C. Radhakrishnan, M. Parthasarathy, S. Jambulingam, T. Byrnes, Sci. Rep. 7, 13865 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    S. Fujimoto, Phys. Rev. Lett. 103, 047203 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    S.A. Owerre, Phys. Rev. B 94, 094405 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    S.A. Owerre, J. Phys. Condens. Matter 29, 385801 (2017)CrossRefGoogle Scholar
  19. 19.
    J.-N. Chazalviel, Phys. Rev. B 11, 3918 (1975)ADSCrossRefGoogle Scholar
  20. 20.
    M. Idrish Miah, J. Phys. D: Appl. Phys. 40, 1659 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    Y. Shiomi, M. Mochizuki, Y. Kaneko, Y. Tokura, Phys. Rev. Lett. 108, 056601 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958)ADSCrossRefGoogle Scholar
  23. 23.
    T. Moriya, Phys. Rev. 120, 91 (1960)ADSCrossRefGoogle Scholar
  24. 24.
    I. Affleck, M. Oshikawa, Phys. Rev. B 60, 1038 (1999)ADSCrossRefGoogle Scholar
  25. 25.
    M. Oshikawa, I. Affleck, Phys. Rev. Lett. 79, 2883 (1997)ADSCrossRefGoogle Scholar
  26. 26.
    L.S. Lima, Phys. Status Solidi B 249, 1613 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    L.S. Lima, Phys. Eur. Phys. J. B 86, 99 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    L.S. Lima, A.S.T. Pires, J. Magn. Magn. Mater. 320, 2316 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    L.S. Lima, Physica C 549, 147 (2018)ADSCrossRefGoogle Scholar
  30. 30.
    L.S. Lima, J. Magn. Magn. Mater. 454, 150 (2018)ADSCrossRefGoogle Scholar
  31. 31.
    J.N. Mc Elearney, S. Merchant, Phys. Rev. B 18, 3612 (1978)ADSCrossRefGoogle Scholar
  32. 32.
    Y. Shiomi, M. Mochizuki, Y. Kaneko, Y. Tokura, Phys. Rev. Lett. 108, 056601 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    D. Senechal, http://arXiv:cond-mat/9908262v1 (1999).
  34. 34.
    I. Garate, I. Affleck, Phys. Rev. B 81, 144419 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    A.O. Gogolin, A.A. Nersesyan, A.M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, Cambridge, England, 1998)Google Scholar
  36. 36.
    D. Sellmann, Ph.D. thesis, TU Kaiserslautern, Kaiserslautern 2004Google Scholar
  37. 37.
    P. Calabrense, J. Cardy, J. Stat. Mech.: Theory Exp. 2004, P06002 (2004)Google Scholar
  38. 38.
    E. Fradkin, Field Theories of Condensed Matter Physics, 2nd edn. (Cambridge University Press, Cambridge, UK, 2013)Google Scholar
  39. 39.
    M.P.A. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher, Phys. Rev. B 40, 546 (1989)ADSCrossRefGoogle Scholar
  40. 40.
    M.P.A. Fisher, G. Grinstein, Phys. Rev. Lett. 60, 208 (1988)ADSCrossRefGoogle Scholar
  41. 41.
    S.R. White, Phys. Rev. Lett. 69, 2863 (1992)ADSCrossRefGoogle Scholar
  42. 42.
    S.R. White, Phys. Rev. B 48, 10345 (1993)ADSCrossRefGoogle Scholar
  43. 43.
    S.-J. Gu, H.-Q. Lin, Y.-Q. Li, Phys. Rev. A 68, 042330 (2003)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Física, Centro Federal de Educação Tecnológica de Minas GeraisBelo HorizonteBrazil

Personalised recommendations