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Entanglement in a two-qubit Heisenberg XXX model with x-components of Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions

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Abstract

This article explores the concurrence in a two-qubit Heisenberg XXX model with Dzyaloshinskii–Moriya (DM) and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interactions. The concurrence expression was developed using the physical variables connected with the chosen system. Our results indicate that the temperature, the spin coupling constant, the x-components of the DM and KSEA interactions may all play a role in determining the degree of intricacy between states. Additionally, these findings imply that the separability of states is obtained at high-temperature domains or by switching the spin coupling. In contrast, the entanglement of states may be achieved at low temperatures or by using high values of the x-components of the DM and KSEA parameters. Furthermore, the DM and KSEA interactions have an identical effect on the concurrence behaviors at high temperatures.

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References

  1. Schrödinger, E.: Mathematical Proceedings of the Cambridge Philosophical Society. Proc. Camb. Phil. Soc. 31, 555 (1935)

    Article  ADS  Google Scholar 

  2. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  Google Scholar 

  3. Bell, J.S.: On the Einstein Podolsky Rosen paradox. Physics 1, 195–200 (1964)

    Article  MathSciNet  Google Scholar 

  4. Bennett, C.H., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  5. Murao, M., et al.: Quantum telecloning and multiparticle entanglement. Phys. Rev. A 59, 156 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  6. Grover, L.K.: Quantum computers can search rapidly by using almost any transformation. Phys. Rev. Lett. 80, 4329 (1998)

    Article  ADS  Google Scholar 

  7. Grover, L.K.: Quantum mechanics helps in searching for a needle in a Haystack. Phys. Rev. Lett. 79, 325 (1997)

    Article  ADS  Google Scholar 

  8. Chiara, G.D., et al.: Quantum cloning in spin networks. Phys. Rev. A 70, 062308 (2004)

    Article  ADS  Google Scholar 

  9. Yeo, Y.: Studying the thermally entangled state of a three-qubit Heisenberg XX ring via quantum teleportation. Phys. Rev. A 68, 022316 (2003)

    Article  ADS  Google Scholar 

  10. Trauzettel, B., et al.: Spin qubits in graphene quantum dots. Nat. Phys. 3, 192 (2007)

    Article  Google Scholar 

  11. Kane, B.E.: A silicon-based nuclear spin quantum computer. Nature 393, 133 (1998)

    Article  ADS  Google Scholar 

  12. Sørensen, A., Mølmer, K.: Spin-spin interaction and spin squeezing in an optical lattice. Phys. Rev. Lett. 83, 2274 (1999)

    Article  ADS  Google Scholar 

  13. Nishiyama, M., et al.: Spin triplet superconducting state due to broken inversion symmetry in \(Li_2Pt_3B\). Phys. Rev. Lett. 98, 047002 (2007)

    Article  Google Scholar 

  14. Morra, R.M., et al.: Spin dynamics and the Haldane gap in the spin-1 quasi-one-dimensional antiferromagnet \(CsNiCl_3\). Phys. Rev. B 38, 543 (1988)

    Article  Google Scholar 

  15. Wang, X., Qin, S., Yu, L.: Haldane gap for the \(S=2\) antiferromagnetic Heisenberg chain revisited. Phys. Rev. B 60, 14529 (1999)

    Article  Google Scholar 

  16. Zhou, L., Song, H.S., et al.: Enhanced thermal entanglement in an anisotropic Heisenberg XYZ chain. Phys. Rev. A 68, 024301 (2003)

    Article  ADS  Google Scholar 

  17. Song, W.: Effects of intrinsic decoherence on the entanglement of a two-qutrit 1D optical lattice chain with nonlinear coupling. Chin. Phys. B 18, 3251 (2009)

    Article  ADS  Google Scholar 

  18. Guo, K.T., et al.: Entanglement in a two-spin \((1/2, 3/2)\) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. J. Phys. A Math. Theor. 43, 505301 (2010)

    Article  MathSciNet  Google Scholar 

  19. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  20. Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  21. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  22. Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)

    Article  ADS  Google Scholar 

  23. Jafari, R., Langari, A.: Three-qubits ground state and thermal entanglement of Anisotropic Heisenberg (XXZ) and Ising models with Dzyaloshinskii-Moriya interaction. Int. J. Quantum Inf. 9, 1057 (2011)

    Article  MathSciNet  Google Scholar 

  24. Jafari, R., Kargarian, M., Langari, A., Siahatgar, M.: Phase diagram and entanglement of the Ising model with Dzyaloshinskii-Moriya interaction. Phys. Rev. B 78, 214414 (2008)

    Article  ADS  Google Scholar 

  25. Mehran, E., Mahdavifar, S., Jafari, R.: Publisher’s note: induced effects of the Dzyaloshinskii-Moriya interaction on the thermal entanglement in spin\(-1/2\) Heisenberg chains. Phys. Rev. A 89, 049903 (2014)

    Article  Google Scholar 

  26. Habiballah, N., Khedif, Y., Daoud, M.: Local quantum uncertainty in XYZ Heisenberg spin models with Dzyaloshinskii Moriya interaction. Eur. Phys. J. D 72, 154 (2018)

    Article  ADS  Google Scholar 

  27. Pourkarimi, M.R.: The dynamics of quantum correlations in multi-qubit spin chains under the effect of Dzyaloshinskii-Moriya interaction. Int. J. Theor. Phys. 57, 1158 (2018)

    Article  Google Scholar 

  28. Kamta, G.L., Starace, A.F.: Anisotropy and magnetic field effects on the entanglement of a two Qubit Heisenberg XY chain. Phys. Rev. Lett. 88, 107901 (2002)

    Article  ADS  Google Scholar 

  29. Sun, Y., Ma, X.-P., Guo, J.: Dynamics of non-equilibrium thermal quantum correlation in a two-qubit Heisenberg XYZ model. Quantum Inf. Process. 19, 98 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  30. Canosa, N., Rossignoli, R.: Separability conditions and limit temperatures for entanglement detection in two-qubit Heisenberg XYZ mode. Phys. Rev. A 69, 052306 (2004)

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

    Article  ADS  Google Scholar 

  32. Moriya, T.: New mechanism of Anisotropic superexchange interaction. Phys. Rev. Lett. 4, 228 (1960)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. 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 

  35. Yurischev, M.A.: On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky’s Moriya and Kaplan Shekhtman Entin-Wohlman Aharony interactions. Quantum Inf. Process. 19, 336 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  36. Fedorova, A.V., Yurischev, M.A.: Quantum entanglement in the anisotropic Heisenberg model with multicomponent DM and KSEA interactions. Quantum Inf. Process. 20, 169 (2021)

    Article  MathSciNet  ADS  Google Scholar 

  37. Fu, H., Zhong, M., Tong, P.: The effects of KSEA interaction on the ground-state properties of spin chains in a transverse field. Eur. Phys. J. B 93, 80 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  38. Motamedifar, M.: Dynamical pairwise entanglement and two-point correlations in the three-ligand spin-star structure. Phys. A Stat. Mech. Appl. 483, 280 (2017)

    Article  MathSciNet  Google Scholar 

  39. González-Gutiérrez, C.A., Román-Ancheyta, R., Espitia, D., Franco, R.L.: Relations between entanglement and purity in non-Markovian dynamics. Int. J. Quantum Inf. 14, 1650031 (2016)

    Article  Google Scholar 

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Acknowledgements

Our sincere gratitude goes to Mohamed Monkad, head of the Laboratory for Physics of Condensed Matter (LPMC) in the Faculty of Sciences at Chouaïb Doukkali University, for his essential assistance.

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Authors and Affiliations

  1. LPTHE Laboratory, Faculty of Sciences, Ibn Zohr University, PO Box 8106, Agadir, Morocco

    Rachid Houça

  2. Laboratory L.P.M.C., Team of Theoretical Physics, Department of Physics, Faculty of Sciences, Chouaib Doukkali University, PO Box 20, 24000, El Jadida, Morocco

    Rachid Houça, El Bouâzzaoui Choubabi, Mohammed El Bouziani, Abdelhadi Belouad & Abdellatif Kamal

  3. ISPS2I Laboratory, National Higher School of Arts and Crafts(ENSAM), Hassan II University, 20670, Casablanca, Morocco

    Abdellatif Kamal

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  1. Rachid Houça
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  2. El Bouâzzaoui Choubabi
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  3. Mohammed El Bouziani
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  4. Abdelhadi Belouad
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  5. Abdellatif Kamal
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Correspondence to Rachid Houça.

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Houça, R., Choubabi, E.B., Bouziani, M.E. et al. Entanglement in a two-qubit Heisenberg XXX model with x-components of Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions. Quantum Inf Process 21, 200 (2022). https://doi.org/10.1007/s11128-022-03544-3

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