Thermal Entanglement in the Quantum XXZ Model in Triangular and Bilayer Honeycomb Lattices

  • L. S. LimaEmail author


Thermal entanglement is studied in the frustrated two-dimensional Heisenberg model in triangular and honeycomb lattices employing linear spin waves. Our results display a strong effect of the coupling parameters of next-nearest neighbors interaction \(\alpha =J'/J\) on entanglement at \(T\rightarrow 0\) , where the spin Hall conductivity is nonzero for a value of external field H. We employ linear spin waves to investigate the entanglement with T and next-nearest neighbor interaction \(J'\). For the bilayer honeycomb lattice, we analyze the entanglement as a function of inter-chain coupling \(J^{\perp }\), and in this case we find that the entanglement tends to zero at \(T=0\), where it decreases with \(J^{\perp }\) for higher temperatures.


Thermal entanglement Phase transition Frustrated Heisenberg model 



This work was supported in part by the National Council for Scientific and Technological Development.


  1. 1.
    D.J. Thouless, M. Kohmoto, M.P. Nightingale, M. den Nijs, Phys. Rev. Lett. 49, 405 (1982)ADSCrossRefGoogle Scholar
  2. 2.
    C. Lacroix, P. Mendels, F. Mila, Introduction to Frustrated Magnetism (Springer, Berlin, 2011)CrossRefGoogle Scholar
  3. 3.
    W.H. Zheng, J.O. Fjaerestad, R.R.P. Singh, R.H. McKenzie, R. Coldea, Phys. Rev. B 74, 224420 (2006)ADSCrossRefGoogle Scholar
  4. 4.
    S.R. White, A.L. Chernyshev, Phys. Rev. Lett. 99, 127004 (2007)ADSCrossRefGoogle Scholar
  5. 5.
    A.L. Chernyshev, M.E. Zhitomirsky, Phys. Rev. B 91, 219905(E) (2015)ADSCrossRefGoogle Scholar
  6. 6.
    T. Jolicoeur, E. Dagotto, E. Gagliano, S. Bacci, Phys. Rev. B 42, 4800 (1990)ADSCrossRefGoogle Scholar
  7. 7.
    S.A. Owerre, Phys. Rev. B 94, 094405 (2016)ADSCrossRefGoogle Scholar
  8. 8.
    Y. Shiomi, M. Mochizuki, Y. Kaneko, Y. Tokura, Phys. Rev. Lett. 108, 056601 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    Y. Onosel, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, Y. Tokura, Science 329, 297 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    T. Ideue, Y. Onose, H. Katsura, Y. Shiomi, S. Ishiwata, N. Nagaosa, Y. Tokura, Phys. Rev. B 85, 134411 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    R. Chisnell, J.S. Helton, D.E. Freedman, D.K. Singh, R.I. Bewley, D.G. Nocera, Y.S. Lee, Phys. Rev. Lett. 115, 147201 (2015)ADSCrossRefGoogle Scholar
  12. 12.
    M. Hirschberger, R. Chisnell, Y.S. Lee, N.P. Ong, Phys. Rev. Lett. 115, 106603 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    G. Vidal, J.L. Latorre, E.I. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    A.L. Malvezzi, G. Karpat, B. Cakmak, F.F. Fanchini, T. Debarba, R.O. Vianna, Phys. Rev. B 93, 184428 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    K.H. Norwich, Phys. A 462, 141 (2016)MathSciNetCrossRefGoogle Scholar
  16. 16.
    L.S. Lima, J. Mod. Phys. 06, 2231 (2015)CrossRefGoogle Scholar
  17. 17.
    L.S. Lima, Phys. A 483, 239 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    L.S. Lima, Phys. A 492, 1853 (2018)MathSciNetCrossRefGoogle Scholar
  19. 19.
    L.S. Lima, Eur. Phys. J. D 73, 6 (2019)ADSCrossRefGoogle Scholar
  20. 20.
    T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    A.R. Its, B.-Q. Jin, V.E. Korepin, J. Phys. A: Math. Gen. 38, 2975 (2005)ADSCrossRefGoogle Scholar
  22. 22.
    J.I. Latorre, E. Rico, G. Vidal, Quantum Inf. Comput. 4, 48 (2004)MathSciNetGoogle Scholar
  23. 23.
    S. Fujimoto, Phys. Rev. Lett. 103, 047203 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    A.E. Trumper, Phys. Rev. B 60, 2987 (1999)ADSCrossRefGoogle Scholar
  25. 25.
    L.S. Lima, E.B. Cantuária, G.M. Dinz, Physica C 559, 50 (2019)ADSCrossRefGoogle Scholar
  26. 26.
    S. Sachdev, Quantum Phase Transitions, 2nd edn. (Cambridge University Press, Cambridge, 2011)CrossRefGoogle Scholar
  27. 27.
    L.S. Lima, Solid State Commun. 239, 5 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    D. Bruss, G. Leuchs, Lectures on Quantum Information (Wiley-VCH, Weinheim, 2007)zbMATHGoogle Scholar
  29. 29.
    E. Fradkin, Field Theories of Condensed Matter Physics, 2nd edn. (Cambridge University Press, Cambridge, 2013)CrossRefGoogle Scholar
  30. 30.
    P. Calabrense, J. Cardy, J. Stat. Mech. Theory Exp. 2004, P06002 (2004)Google Scholar
  31. 31.
    D. Bianchini, O.A. Castro-Alvaredo, B. Doyon, E. Levi, F. Ravanini, J. Phys. A: Math. Theor. 48, 04FT01 (2015)CrossRefGoogle Scholar
  32. 32.
    M. Matsuda, M. Azuma, M. Tokunaga, Y. Shimakawa, N. Kumada, Phys. Rev. Lett. 105, 187201 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    S. Okubo, T. Ueda, H. Ohta, W. Zhang, T. Sakurai, N. Onishi, M. Azuma, Y. Shimakawa, H. Nakano, T. Sakai, Phys. Rev. B 82, 064412 (2010)CrossRefGoogle Scholar
  34. 34.
    S.A. Owerre, J. Phys. Condens. Matter. 29, 385801 (2017)CrossRefGoogle Scholar
  35. 35.
    N. Laflorencie, Phys. Rep. 646, 1 (2016)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of PhysicsFederal Center for Technological Education of Minas GeraisBelo HorizonteBrazil

Personalised recommendations