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Effect of Dzialoshinski-Moriya interaction on thermal entanglement of a mixed-spin chain

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Abstract

The effect of Dzialoshinski-Moriya (DM) interaction on thermal entanglement of a mixed-spin chain in an external magnetic field is investigated. It is found that DM interaction may enhance quantum thermal entanglement to a maximal value even though the magnetic field plays a positive role in shrinking thermal entanglement in the mixed-spin chain. Furthermore, the effect of inhomogeneity of the magnetic field on quantum entanglement is analyzed. Our analysis will shed some light on the understanding of the effect of the DM interaction on thermal entanglement of a mixed-spin chain.

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References

  1. Bennett C H. Quantum cryptography using any two nonorthogonal states. Phys Rev Lett, 1992, 68: 3121–3124

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. Bennett C H, Brassard G, Crepeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett, 1993, 70: 1895–1899

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. Bennett C H, DiVincenzo D P. Quantum information and computation. Nature, 2000, 404: 247–255

    Article  ADS  Google Scholar 

  4. Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. 1st ed. Cambridge: Cambridge Univ Press, 2000. 571–574

    MATH  Google Scholar 

  5. Wootters W K. Entanglement of Formation of An Arbitrary State of Two Qubits. Phys Rev Lett, 1998, 80: 2245–2248

    Article  ADS  Google Scholar 

  6. Bouwmeester D, Pan J W, Daniell M, et al. Observation of three-photon Greenberger-Horne-Zeilinger entanglement. Phys Rev Lett, 1999, 82: 1345–1349

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. Raschenbeutel A, Nogues G, Osnaghi S, et al. Step-by-step engineered multi-particle entanglement. Science, 2000, 288: 2024–2028

    Article  ADS  Google Scholar 

  8. Ye M Y, Zhang Y S, Guo G C. Quantum entanglement and quantum operation. Sci China Ser G-Phys Mech Astron, 2008, 51(1): 14–21

    Article  MATH  ADS  Google Scholar 

  9. Ding S C, Jin Z. Review on the study of entanglement in quantum computation speedup. Chin Sci Bull, 2007, 52(16): 2161–2166

    Article  Google Scholar 

  10. Wang X G. Entanglement in the quantum Heisenberg XY model. Phys Rev A, 2001, 64: 012313

    Article  ADS  Google Scholar 

  11. Wang X G, Zanardi P. Effects of anisotropy on thermal entanglement. Phys Lett A, 2001, 281: 101–104

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. Wang X G, Zanardi P. Quantum entanglement and Bell inequalities in Heisenberg spin chains. Phys Lett A, 2001, 301: 1–6

    Article  ADS  MathSciNet  Google Scholar 

  13. Wang X G. Threshold temperature for pairwise and many-particle thermal entanglement in the isotropic Heisenberg model. Phys Rev A, 2002, 66: 044305

    Article  ADS  Google Scholar 

  14. Wang X G, Li H B, Sun Z, et al. Entanglement in spin-1 Heisenberg chains. J Phys A: Math Gen, 2005, 38: 8703–8714

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Gunlycke D, Kendon V M, Vedral V, et al. Thermal concurrence mixing in a one-dimensional Ising model. Phys Rev A, 2001, 64: 042302

    Article  ADS  Google Scholar 

  16. Hao X, Zhu S Q. Entanglement in a spin-s antiferromagnetic Heisenberg chain. Phys Rev A, 2005, 72: 042306

    Article  ADS  Google Scholar 

  17. Wang X G, Wang Z D, Thermal entanglement in ferrimagnetic chains. Phys Rev A, 2006, 73: 064302

    Article  ADS  Google Scholar 

  18. Rossognoli R, Canosa N. Limit temperature for entanglement in generalized statistics. Phys Lett A, 2004, 323: 22–28

    Article  ADS  MathSciNet  Google Scholar 

  19. Rossognoli R, Canosa N. Global thermal entanglement in n-qubit systems. Phys Rev A, 2005, 72: 012335

    Article  ADS  Google Scholar 

  20. Nielsen M A. Quantum information theory. 2000, arxiv: quant-ph/0011036

  21. Liu D, Zhang Y, Long G L. Influence of magnetic current on the ground state entanglement in an isotropic transverse XY chain. Prog Nat Sci, 2007, 17(10): 1147–1151

    Google Scholar 

  22. Hu M L, Tian D P. Effects of impurity on the entanglement of the three-qubit Heisenberg XXX spin chain. Sci China Ser G-Phys Mech Astron, 2007, 50(2): 208–214

    Article  MATH  Google Scholar 

  23. Dzialoshinski I. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J Phys Chem Solids, 1958, 4: 241–255

    Article  ADS  Google Scholar 

  24. Moriya T. New mechanism of anisotropic superexchange interaction. Phys Rev Lett, 1960, 4: 228–230

    Article  ADS  Google Scholar 

  25. Moriya T. Theory of magnetism of NiF2. Phys Rev, 1960, 117: 635–647

    Article  ADS  Google Scholar 

  26. Moriya T. Anisotropic superexchange interaction and weak ferromagnetism. Phys Rev, 1960, 120: 91–98

    Article  ADS  Google Scholar 

  27. Zhang G F. Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction. Phys Rev A, 2007, 75: 034304

    Article  ADS  Google Scholar 

  28. Gurkan, Nilhan Z, Pashaev, et al. Two-qubit entanglement in XYZ magnetic chain with DM antisymmetric anisotropic exchange interaction. 2007, arxiv: quant-ph/0705.0679

  29. van Koningsbruggen P J, Kahn O, Nakatani K, et al. Magnetism of A-copper (II) bimetallic chain compounds (A = iron, cobalt, nickel): One-and three-dimensional behaviors. Inorg Chem, 1990, 29: 3325–3331

    Article  Google Scholar 

  30. Hao X, Zhu S Q. Entanglement in a quantum mixed-spin chain. Phys Lett A, 2007, 366: 206–210

    Article  ADS  MathSciNet  Google Scholar 

  31. Zyczkowski K, Horodecki P, Sanpera A, et al. Volume of the set of separable states. Phys Rev A, 1998, 58: 883–892

    Article  ADS  MathSciNet  Google Scholar 

  32. Peres A. Separability criterion for density matrices. Phys Rev Lett, 1996, 77: 1413–1415

    Article  MATH  ADS  MathSciNet  Google Scholar 

  33. Vidal G, Werner R R. Computable measure of entanglement. Phys Rev A, 2002, 65: 032314

    Article  ADS  Google Scholar 

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Correspondence to XiaoSan Ma.

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Supported by the National Natural Science Foundation of China (Grant No. 60573008) and Anhui Foundation for Young Teachers (Grant No. 2008jq1025zd)

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Ma, X., Zhang, J., Cong, H. et al. Effect of Dzialoshinski-Moriya interaction on thermal entanglement of a mixed-spin chain. Sci. China Ser. G-Phys. Mech. Astron. 51, 1897–1904 (2008). https://doi.org/10.1007/s11433-008-0191-6

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  • DOI: https://doi.org/10.1007/s11433-008-0191-6

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