Skip to main content
SpringerLink
Log in

Influence of Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions on quantum entanglement in a two-qubit Heisenberg XYZ chain

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

This paper investigates quantum entanglement in a two-qubit Heisenberg XYZ system with Kaplan–Shekhtman–Entin–Wohlman–Aharony and Dzyaloshinskii–Moriya couplings along the x-axis. By the concept of concurrence, the effects of these two types of interactions on thermal entanglement are studied in detail for both antiferromagnetic and ferromagnetic cases. By setting the strengths coupling of the spin, we quickly recover the Ising and XXX Heisenberg models. Additionally, we find that the influence of Kaplan–Shekhtman–Entin–Wohlman–Aharony and Dzyaloshinskii–Moriya couplings can enhance entanglement and influence the critical temperature beyond the entanglement vanishes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

Not applicable.

Code Avaliability

Not applicable.

References

  1. Gallager, R.G.: Information Theory and Reliable Communication. John Wiley Sons. Inc, New York (1968)

    MATH  Google Scholar 

  2. Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991)

    Book  MATH  Google Scholar 

  3. Kay, S.M.: Fundamentals of Statistical Signal Processing : Estimation Theory. Prentice Hall, Englewood Cliffs (1993)

    MATH  Google Scholar 

  4. Kay, S.M.: Fundamentals of Statistical Signal Processing : Detection Theory. Prentice Hall, Englewood Cliffs (1998)

    Google Scholar 

  5. Mohamed, A.B.A., Eleuch, H.: Optical tomography dynamics induced by qubit-resonator interaction under intrinsic decoherence. Sci. Rep. 12, 17162 (2022)

    Article  ADS  Google Scholar 

  6. Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976)

    MATH  Google Scholar 

  7. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  8. Desurvire, E.: Classical and Quantum Information Theory. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  9. Wilde, M.M.: Quantum Information Theory. Cambridge University Press, Cambridge (2013)

    Book  MATH  Google Scholar 

  10. Bell, J.S.: On the einstein podolsky rosen paradox. Physics Physique Fizika. 1, 195 (1964)

    Article  MathSciNet  Google Scholar 

  11. Hsieh, M.H., Wilde, M.M.: Entanglement-assisted communication of classical and quantum information. IEEE Transactions on Information Theory. 56, 4682–4704 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Aspect, A., Grangier, P., Roger, G.: Experimental tests of realistic local theories via Bell’s theorem. Phys. Rev. Lett. 47, 460 (1981)

    Article  ADS  Google Scholar 

  13. Aspect, A., Grangier, P., Roger, G.: Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: a new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91 (1982)

    Article  ADS  Google Scholar 

  14. Aspect, A., Dalibard, J., Roger, G.: Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  15. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656 (1996)

    Article  ADS  Google Scholar 

  17. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: eleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett., 70, 1895 (1993)

  18. Bae, J., Jin, J., Kim, J., Yoon, C., Kwon, Y.: Three-party quantum teleportation with asymmetric states. Chaos Solitons Fractals 24, 1047 (2005)

    Article  ADS  MATH  Google Scholar 

  19. Houça, R., Belouad, A., Choubabi, E.B., Kamal, A., El Bouziani, M.: Quantum teleportation via a two-qubit Heisenberg XXX chain with x-component of Dzyaloshinskii-Moriya interaction. J. Magn. Magn. Mater. 563, 169816 (2022)

    Article  MATH  Google Scholar 

  20. Dagotto, E., Rice, T.M.: Surprises on the way from 1D to 2D quantum magnets: the novel ladder materials. Science 271, 618 (1996)

    Article  ADS  Google Scholar 

  21. Ishikawa, Y., Shirane, G., Tarvin, J., Kohgi, M.: Magnetic excitations in the weak itinerant ferromagnet MnSi. Phys. Rev. B 16, 4956 (1977)

  22. Lebech, B., Bernhard, J., Flertoft, T.: Magnetic structures of cubic FeGe studied by small-angle neutron scattering. J. Phys. Condens. Matter 1, 6105 (1989)

    Article  ADS  Google Scholar 

  23. Zheludev, A., et al.: Experimental evidence for kaplan-shekhtman-entin-wohlman-aharony interactions in \(Ba_2CuGe_2O_7\). Phys. Rev. Lett. 81, 5410–5413 (1998)

    Article  ADS  Google Scholar 

  24. Kataev, V., et al.: Strong Anisotropy of Superexchange in the Copper-Oxygen Chains of \(La_{14-x}Ca_xCu_{24}O_{41}\). Phys. Rev. Lett. 86, 2882 (2001)

    Article  ADS  Google Scholar 

  25. Tsukada, I., Takeya, J., Masuda, T., Uchinokura, K.: Weak ferromagnetism of quasi-one-dimensional \(S=\frac{1}{2}\) antiferromagnet. Phys. Rev. B 62, 6061 (2000)

    Article  ADS  Google Scholar 

  26. Dzyaloshinskii, I.: A thermodynamic theory of weak ferromagnetism of antiferromagnetics. Phys. Chem. Solids 4, 241 (1958)

    Article  ADS  Google Scholar 

  27. Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91 (1960)

    Article  ADS  Google Scholar 

  28. Shekhtman, L., Entin-Wohlman, O., Aharony, A.: Moriya anisotropic superexchange interaction, frustration, and Dzyaloshinsky’s weak ferromagnetism. Phys. Rev. Lett. 69, 836 (1992)

    Article  ADS  Google Scholar 

  29. Shekhtman, L., Aharony, A., Entin-Wohlman, O.: Bond-dependent symmetric and antisymmetric superexchange interactions in \(La_2CuO_4\). Phys. Rev. B 47, 174 (1993)

    Article  ADS  Google Scholar 

  30. Kaplan, T.A.: Single-band Hubbard model with spin-orbit coupling. Z. Phys. B 49, 313 (1983)

    Article  ADS  Google Scholar 

  31. Mohamed, A.B.A., Rahman, A., Aldosari, F.M.: Thermal quantum memory, Bell-non-locality, and entanglement behaviors in a two-spin Heisenberg chain model. Alex. Eng. J. 66, 861–871 (2023)

    Article  Google Scholar 

  32. Mohamed, A.B.A., Eleuch, H.: Thermal local Fisher information and quantum uncertainty in Heisenberg model. Phys. Scr. 97, 095105 (2022)

    Article  ADS  Google Scholar 

  33. Houça, R., Belouad, A., Choubabi, E.B., Kamal, A., El Bouziani, M.: Entanglement in a two-qubit Heisenberg XXX model with x-components of Dzyaloshinskii-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions. Quant. Infor. Proc. 21, 1 (2022)

    MathSciNet  MATH  Google Scholar 

  34. Mohamed, A.B.A.: Pairwise quantum correlations of a three-qubit XY chain with phase decoherence. Quantum. Inf. Process. 12, 1141–1153 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Moqine, Y., Adnane, B., Belouad, A., Belhouideg, S., Houça, R.: Local quantum uncertainty of a two-qubit XY Heisenberg model with different Dzyaloshinskii-Moriya couplings. Int. J. Quantum Inf. (2023). https://doi.org/10.1142/S0219749923400075

    Article  MATH  Google Scholar 

  36. Mohamed, A.B.A., Farouk, A., Mansour, F.Y., Eleuch, H.: Quantum correlation via skew information and bell function beyond entanglement in a two-qubit Heisenberg XYZ model: effect of the phase damping. Appl. Sci. 10, 3782 (2020)

    Article  Google Scholar 

  37. Wang, Z.G., Chen, Y.G., Chen, H., Liu. H.L., Shi, Y.L.: The symmetric and antisymmetric superexchange interactions in spin-Peierls system. Acta. Phys. Sin. 54, 2329 (2005)

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. LPMC. Laboratory, Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University, PO Box 20, 24000, El Jadida, Morocco

    Brahim Adnane, Rachid Houça, Abdelhadi Belouad & El Bouâzzaoui Choubabi

  2. Research Laboratory of Physics and Engineers Sciences, Team of Applied Physics and New Technologies, Polydisciplinary Faculty, Sultan Moulay Slimane University, Béni Mellal, Morocco

    Younes Moqine

  3. LPTHE. Laboratory, Theoretical Physics and High Energy, Faculty of Sciences, Ibn Zohr University, PO Box 8106, Agadir, Morocco

    Rachid Houça

Authors
  1. Brahim Adnane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Younes Moqine
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rachid Houça
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abdelhadi Belouad
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. El Bouâzzaoui Choubabi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rachid Houça.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Adnane, B., Moqine, Y., Houça, R. et al. Influence of Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions on quantum entanglement in a two-qubit Heisenberg XYZ chain. Quantum Inf Process 22, 225 (2023). https://doi.org/10.1007/s11128-023-03974-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-03974-7

Keywords

Search

Navigation