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Effect of Dzyaloshinskii–Moriya interaction on quantum entanglement in superconductors models of high Tc

  • Leonardo S. LimaEmail author
Regular Article
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Abstract

The modified spin-wave (MSW) theory and SU(N) Schwinger boson theory (SBW) are employed to study the quantum entanglement in one- (1D) and two-dimensional (2D) Heisenberg antiferromagnets with Dzyaloshinskii–Moriya (DM) interaction which are models to superconducting materials of high critical temperature Tc such as La2CuO4. For the 1D case, we consider integer spin and for 2D case, since the behavior is independent on the spin value, we consider the one-half-spin and square lattice. We get the entanglement entropy in function of the temperature T where we have not gotten large variation of the quantum entanglement with the changing of the anisotropy Δ and DM interaction constant D.

Graphical abstract

Keywords

Quantum Information 

References

  1. 1.
    D.J. Scalapino, in Handbook of High-Temperature Superconductivity, edited by J.R. Schrieffer, J.S. Brooks (Springer, New York, 2007) Google Scholar
  2. 2.
    S. Sachdev, Science 336, 1510 (2012) ADSCrossRefGoogle Scholar
  3. 3.
    L.S. Lima, Solid State Commun. 258, 21 (2017) ADSCrossRefGoogle Scholar
  4. 4.
    L.S. Lima, Physica C 527, 33 (2016) ADSCrossRefGoogle Scholar
  5. 5.
    F. Iemini, T.O. Maciel, R.O. Vianna, Phys. Rev. B 92, 075423 (2015) ADSCrossRefGoogle Scholar
  6. 6.
    F. Iemini, L. da Silva Souza, T. Debarba, A.T. Cesario, T.O. Maciel, R.O. Vianna, Eur. Phys. J. D 71, 119 (2017) ADSCrossRefGoogle Scholar
  7. 7.
    K.H. Norwich, Physica A 462, 141 (2016) ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    L.S. Lima, J. Mod. Phys. 06, 2231 (2015) CrossRefGoogle Scholar
  9. 9.
    L.S. Lima, Physica A 483, 239 (2017) ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    L.S. Lima, Physica A 492, 1853 (2018) ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966) ADSCrossRefGoogle Scholar
  12. 12.
    F.D.M. Haldane, Phys. Rev. Lett. 50, 1153 (1983) ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    F.D.M. Haldane, Phys. Lett. A 93, 464 (1983) ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 16, 407 (1961) ADSCrossRefGoogle Scholar
  15. 15.
    E.H. Lieb, D. Mattis, J. Math. Phys. 3, 749 (1962) ADSCrossRefGoogle Scholar
  16. 16.
    L.S. Lima, A.S.T. Pires, J. Magn. Magn. Mater. 322, 2157 (2010) ADSCrossRefGoogle Scholar
  17. 17.
    A.R. Pereira, S.A. Leonel, P.Z. Coura, B.V. Costa, Phys. Rev. B 71, 014403 (2005) ADSCrossRefGoogle Scholar
  18. 18.
    T. Roscilde, S. Haas, Phys. Rev. Lett. 99, 047205 (2007) ADSCrossRefGoogle Scholar
  19. 19.
    L.S. Lima, A.S.T. Pires, B.V. Costa, Physica A 438, 579 (2015) ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    L.S. Lima, A.S.T. Pires, B.V. Costa, J. Magn. Magn. Mater. 371, 89 (2014) ADSCrossRefGoogle Scholar
  21. 21.
    A.S.T. Pires, L.S. Lima, Phys. Rev. B 79, 064401 (2009) ADSCrossRefGoogle Scholar
  22. 22.
    A. Einstein, E. Podolsky, N. Rosen, Phys. Rev. 47, 777 (1935) ADSCrossRefGoogle Scholar
  23. 23.
    A. Metavitsiadis, D. Sellmann, S. Eggert, Phys. Rev. B, 89, 241104 (2014) ADSCrossRefGoogle Scholar
  24. 24.
    A.L. de Paula, J.G.G. de Oliveira, J.G. Peixoto de Faria, D.S. Freitas, M.C. Nemes, Phys. Rev. A 89, 022303 (2014) ADSCrossRefGoogle Scholar
  25. 25.
    A.F. Kracklauer, J. Mod. Phys. 6, 1961 (2015) CrossRefGoogle Scholar
  26. 26.
    G. Vidal, J.L. Latorre, E.I. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003) ADSCrossRefGoogle Scholar
  27. 27.
    A.L. Malvezzi, G. Karpat, B. Cakmak, F.F. Fanchini, T. Debarba, R.O. Vianna, Phys. Rev. B 93, 184428 (2016) ADSCrossRefGoogle Scholar
  28. 28.
    T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002) ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    A.R. Its, B.-Q. Jin, V.E. Korepin, J. Phys. A: Math. Gen. 38, 2975 (2005) ADSCrossRefGoogle Scholar
  30. 30.
    J.I. Latorre, E. Rico, G. Vidal, Quant. Inf. Comput. 4, 48 (2004) Google Scholar
  31. 31.
    S. Sachdev, Quantum Phase Transitions, 2nd edn. (Cambridge, UK, 2011) Google Scholar
  32. 32.
    D. Bruss, G. Leuchs, Lectures on Quantum Information (WLEY-VCH Verlag, Weinheim, Germany, 2007) Google Scholar
  33. 33.
    E. Fradkin, Field Theories of Condensed Matter Physics, 2nd edn. (Cambridge, UK, 2013) Google Scholar
  34. 34.
    P. Calabrense, J. Cardy, J. Stat. Mech.: Theory Exp. 2004, P06002 (2004) Google Scholar
  35. 35.
    D. Bianchini, O.A. Castro-Alvaredo, B. Doyon, E. Levi, F. Ravanini, J. Phys. A: Math. Theor. 48, 04FT01 (2015) CrossRefGoogle Scholar
  36. 36.
    A.S.T. Pires, M.E. Gouvea, J. Magn. Magn. Mater. 241, 31 (2002) CrossRefGoogle Scholar
  37. 37.
    L.S. Lima, A.S.T. Pires, J. Phys.: Condens. Matter 19, 436218 (2007) Google Scholar
  38. 38.
    L.S. Lima, Eur. Phys. J. B 93, 99 (2013) ADSCrossRefGoogle Scholar
  39. 39.
    L.S. Lima, Physica B 437, 28 (2014) ADSCrossRefGoogle Scholar
  40. 40.
    M. Takahashi, Phys. Rev. B 40, 2494 (1989) ADSCrossRefGoogle Scholar
  41. 41.
    D.P. Arovas, A. Auerbach, Phys. Rev. B 38, 316 (1988) ADSCrossRefGoogle Scholar
  42. 42.
    A. Auerbarch, Interacting Electrons and Quantum Magnetism (Springer, New York, 1994) Google Scholar
  43. 43.
    I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958) ADSCrossRefGoogle Scholar
  44. 44.
    T. Moriya, Phys. Rev. 120, 91 (1960) ADSCrossRefGoogle Scholar
  45. 45.
    I. Affleck, M. Oshikawa, Phys. Rev. B 60, 1038 (1999) ADSCrossRefGoogle Scholar
  46. 46.
    M. Oshikawa, I. Affleck, Phys. Rev. Lett. 79, 2883 (1997) ADSCrossRefGoogle Scholar
  47. 47.
    I. Garate, I. Affleck, Phys. Rev. B 81, 144419 (2010) ADSCrossRefGoogle Scholar
  48. 48.
    L.S. Lima, Phys. Status Solidi B 249, 1613 (2012) ADSCrossRefGoogle Scholar
  49. 49.
    L.S. Lima, A.S.T. Pires, J. Magn. Magn. Mater. 320, 2316 (2008) ADSCrossRefGoogle Scholar
  50. 50.
    L.S. Lima, Physica C 549, 147 (2018) ADSCrossRefGoogle Scholar
  51. 51.
    L.S. Lima, J. Magn. Magn. Mater. 454, 150 (2018) ADSCrossRefGoogle Scholar
  52. 52.
    U. Schotte, A. Kelnberger, N. Stusser, J. Phys.: Condens. Matter 10, 6391 (1998) ADSGoogle Scholar
  53. 53.
    A.E. Jacobs, T. Nikuni, J. Phys.: Condens. Matter 10, 6405 (1998) ADSGoogle Scholar
  54. 54.
    D.N. Aristov, S.V. Maleyev, Phys. Rev. B 62, R751 (2000) ADSCrossRefGoogle Scholar
  55. 55.
    C.J. De Leone, G.T. Zimanyi, Phys. Rev. B 49, 1131 (1994) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, 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

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