The European Physical Journal D

, Volume 57, Issue 1, pp 123–128 | Cite as

Evolution of entanglement in the Heisenberg XY model: the Yangian algebra method

Quantum Information

Abstract

We construct transition operators in terms of generators for Yangian and act with them on the entangled state of the Heisenberg XY model. Different parameter values of the transition operators lead to different evolutions of the entanglement degree of the final states. It is interesting and worth noting that for some special parameters in the transition operators, our calculation is in good agreement with the experiment. This result sheds a new light on the physics of Y(sl(2)) in quantum information.

Keywords

Transition Operator Entangle State Maximally Entangle State Degeneracy Point Heisenberg Interaction 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Cabello, A. Rossi, G. Vallone, F. De Martini, P. Mataloni, Phys. Rev. Lett. 102, 040401 (2009) Google Scholar
  2. M.R. Beran, S.M. Cohen, Phys. Rev. A 79, 032307 (2009) Google Scholar
  3. P. Skrzypczyk, N. Brunner, S. Popescu, Phys. Rev. Lett. 102, 110402 (2009) Google Scholar
  4. E.T. Campbell, S.C. Benjamin, Phys. Rev. Lett. 101, 130502 (2008) Google Scholar
  5. W. Rosenfeld, S. Berner, J. Volz, M. Weber, H. Weinfurter, Phys. Rev. Lett. 98, 050504 (2007) Google Scholar
  6. J. Niset, J. Fiurasek, N.J. Cerf, Phys. Rev. Lett. 102, 120501 (2009) Google Scholar
  7. W. Yao, R.-B. Liu, L.J. Sham, Phys. Rev. Lett. 95, 030504 (2005) Google Scholar
  8. S. Perseguers, J.I. Cirac, A. Acin, M. Lewenstein, J. Wehr, Phys. Rev. A 77, 022308 (2008) Google Scholar
  9. V. Karimipour, Z. Meghdadi, L. Memarzadeh, Phys. Rev. A 79, 032321 (2009) Google Scholar
  10. J. Kempe, Contemp. Phys. 44, 307 (2003) Google Scholar
  11. A.P. Hines, P.C.E. Stamp, Phys. Rev. A 75, 062321 (2007) Google Scholar
  12. D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998) Google Scholar
  13. G. Burkard, D. Loss, D.P. DiVincenzo, Phys. Rev. B 59, 2070 (1999) Google Scholar
  14. D.A. Lidar, D. Bacon, K.B. Whaley, Phys. Rev. Lett. 82, 4556 (1999) Google Scholar
  15. D.P. DiVincenzo, D. Bacon, J. Kempe, G. Burkard, K.B. Whaley, Nature 408, 339 (2000) Google Scholar
  16. Y. Sun, Y. Chen, H. Chen, Phys. Rev. A 68, 044301 (2003) Google Scholar
  17. F. Kheirandish, S.J. Akhtarshenas, H. Mohammadi, Phys. Rev. A 77, 042309 (2008) Google Scholar
  18. A. Abliz, H.J. Gao, X.C. Xie, Y.S. Wu, W.M. Liu, Phys. Rev. A 74, 052105 (2006) Google Scholar
  19. S.C. Benjamin, S. Bose, Phys. Rev. Lett. 90, 247901 (2003) Google Scholar
  20. S.C. Benjamin, S. Bose, Phys. Rev. A 70, 032314 (2004) Google Scholar
  21. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998) Google Scholar
  22. X.G. Wang, Phys. Rev. A 64, 012313 (2001) Google Scholar
  23. X.G. Wang, H.C. Fu, A.I. Solomon, J. Phys. A: Math. Gen. 34, 11307 (2001) Google Scholar
  24. H.C. Fu, A.I. Solomon, X.G. Wang, J. Phys. A: Math. Gen. 35, 4293 (2002) Google Scholar
  25. J.L. Chen, K. Xue, M.L. Ge, Phys. Rev. A 76, 042324 (2007) Google Scholar
  26. M.G. Hu, K. Xue, M.L. Ge, Phys. Rev. A 78, 052324 (2008) Google Scholar
  27. V.G. Drinfeld, Sov. Math. Dokl. 32, 32 (1985) Google Scholar
  28. V.G. Drinfeld, Quantum Group (PICM, Berkely, 1986), p. 269 Google Scholar
  29. V.G. Drinfeld, Sov. Math. Dokl. 36, 212 (1985) Google Scholar
  30. P.P. Kulish, E.K. Slyanin, Integrable Quantum Field Theories, Lecture Notes in Physics, Vol. 151 (Springer, Berlin, 1982), 61C119 Google Scholar
  31. D.B. Vglov, V.E. Korepin, Phys. Lett. A 190, 238 (1994) Google Scholar
  32. V. Chari, A. Pressley, A Guide to Quantum Groups (Cambridge University Press, Cambridge, 1994) Google Scholar
  33. M.D. Shaw, J.F. Schneiderman, J. Bueno, B.S. Palmer, P. Delsing, P.M. Echternach, Phys. Rev. B 79, 014516 (2009) Google Scholar
  34. F. Kheirandish, S.J. Akhtarshenas, H. Mohammadi, Phys. Rev. A 77, 042309 (2008) Google Scholar
  35. M.L. Ge, K. Xue, Y.M. Cho, Phys. Lett. A 249, 358 (1998) Google Scholar
  36. A.I. Molev, Yangians and Classical Lie algebras, Mathematical Surveys and Monographs (American Mathematical Society, Providence, RI, 2007), Vol. 143 Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of PhysicsShanghai UniversityShanghaiP.R. China
  2. 2.Shanghai Key Lab for AstrophysicsShanghaiP.R. China

Personalised recommendations