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Quantum speed limit for a central system in Lipkin-Meshkov-Glick bath

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Abstract

We investigate the physical feature of quantum phase transition (QPT) in a Lipkin-Meshkov-Glick (LMG) model by calculating the quantum speed limit (QSL) time for a central qubit coupled to a LMG bath. We propose that with a suitable choice of the number of spins in bath and the coupling strength between central system and environment, the transition from no speed-up to speed-up of the open system evolution can be achieved at the QPT point, so the QSL is a potential candidate for witnessing QPT of a LMG model. By considering the physical reason for the acceleration, we study the non-Markovianity of the open system and verify that the non-Markovian property can induce the decrease of evolution time, which is also an indication that the phase transition of the system from Markovian to non-Markovian could occur at the QPT point.

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References

  1. S. Lloyd, Nature 406, 1047 (2000)

    Article  ADS  Google Scholar 

  2. S. Guerin, V. Hakobyan, H.R. Jauslin, Phys. Rev. A 84, 013423 (2011)

    Article  ADS  Google Scholar 

  3. P.M. Poggi, F.C. Lombardo, D.A. Wisniacki, Phys. Rev. A 87, 022315 (2013)

    Article  ADS  Google Scholar 

  4. V. Mukherjee, A. Carlini, A. Mari, T. Caneva, S. Montangero, T. Calarco, R. Fazio, V. Giovannetti, Phys. Rev. A 88, 062326 (2013)

    Article  ADS  Google Scholar 

  5. G.C. Hegerfeldt, Phys. Rev. A 90, 032110 (2014)

    Article  ADS  Google Scholar 

  6. C. Avinadav, R. Fischer, P. London, D. Gershoni, Phys. Rev. B 89, 245311 (2014)

    Article  ADS  Google Scholar 

  7. L. Mandelstam, I.G. Tamm, J. Phys. 9, 249 (1945)

    MathSciNet  Google Scholar 

  8. G.N. Fleming, Nuovo Cimento A 16, 232 (1973)

    Article  ADS  Google Scholar 

  9. K. Bhattacharyya, J. Phys. A 16, 2993 (1983)

    Article  ADS  Google Scholar 

  10. J. Anandan, Y. Aharonov, Phys. Rev. Lett. 65, 169 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  11. N. Margolus, L.B. Levitin, Physica D 120, 188 (1998)

    Article  ADS  Google Scholar 

  12. M.M. Taddei, B.M. Escher, L. Davidovich, R.L. de Matos Filho, Phys. Rev. Lett. 110, 050402 (2013)

    Article  ADS  Google Scholar 

  13. A. del Campo, I.L. Egusquiza, M.B. Plenio, S.F. Huelga, Phys. Rev. Lett. 110, 050403 (2013)

    Article  ADS  Google Scholar 

  14. S. Deffner, E. Lutz, Phys. Rev. Lett. 111, 010402 (2013)

    Article  ADS  Google Scholar 

  15. Y.J. Zhang, W. Han, Y.J. Xia, J.P. Cao, H. Fan, Sci. Rep. 4, 4890 (2013)

    Google Scholar 

  16. Z.Y. Xu, S. Luo, W.L. Yang, C. Liu, S. Zhu, Phys. Rev. A 89, 012307 (2014)

    Article  ADS  Google Scholar 

  17. C. Liu, Z.Y. Xu, S.Q. Zhu, Phys. Rev. A 91, 022102 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  18. Y.J. Zhang, W. Han, Y.J. Xia, J.P. Cao, H. Fan, Phys. Rev. A 91, 032112 (2015)

    Article  ADS  Google Scholar 

  19. L. Hou, B. Shao, Y.B. Wei, J. Zou, J. Phys. A 48, 495302 (2015)

    Article  Google Scholar 

  20. A.D. Cimmarusti, Z. Yan, B.D. Patterson, L.P. Corcos, L.A. Orozco, S. Deffner, Phys. Rev. Lett. 114, 233602 (2015)

    Article  ADS  Google Scholar 

  21. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2001)

  22. H.T. Quan, Z. Song, X.F. Liu, P. Zanardi, C.P. Sun, Phys. Rev. Lett. 96, 140604 (2006).

    Article  ADS  Google Scholar 

  23. R. Dilllenchneider, Phys. Rev. B 78, 224413 (2008)

    Article  ADS  Google Scholar 

  24. M.S. Sarandy, Phys. Rev. A 80, 022108 (2009)

    Article  ADS  Google Scholar 

  25. L.C. Wang and X.X. Yi, Eur. Phys. J. D 57, 281 (2010)

    Article  ADS  Google Scholar 

  26. T. Werlang, C. Trippe, G.A.P. Ribeiro, G. Rigolin, Phys. Rev. Lett. 105, 095702 (2010)

    Article  ADS  Google Scholar 

  27. B.Q. Liu, S. Bin, J. Zou, Phys. Rev. A 82, 062119 (2010)

    Article  ADS  Google Scholar 

  28. I. Bose, A.K. Pal, Int. J. Mod. Phys. B 27, 1345042 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  29. W.W. Cheng, J.X. Li, C.J. Shan, L.Y. Gong, S.M. Zhao, Physica A 398, 1 (2014)

    Article  ADS  Google Scholar 

  30. C.C. Liu, S. Xu, J. He, L. Ye, Ann. Phys. 356, 417 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  31. A. del Campo, M.M. Rams, W.H. Zurek, Phys. Rev. Lett. 109, 115703 (2012)

    Article  ADS  Google Scholar 

  32. H.J. Lipkin, N. Meshkov, A.J. Glick, Nucl. Phys. 62, 188 (1965)

    Article  MathSciNet  Google Scholar 

  33. D.A. Garanin, X. Martínez Hidalgo, E.M. Chudnovsky, Phys. Rev. B 57, 13639 (1998)

    Article  ADS  Google Scholar 

  34. J.I. Cirac, M. Lewenstein, K. Mølmer, P. Zoller, Phys. Rev. A 57, 1208 (1998)

    Article  ADS  Google Scholar 

  35. E.M. Chudnovsky, L. Gunther, Phys. Rev. Lett. 60, 661 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  36. J. Links, H.Q. Zhou, R.H. McKenzie, M.D. Gould, J. Phys. A 36, R63 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. G. Ortiz, R. Somma, J. Dukelsky, S. Rombouts, Nucl. Phys. B 707, 421 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. P. Ribeiro, J. Vidal, R. Mosseri, Phys. Rev. E 78, 021106 (2008)

    Article  ADS  Google Scholar 

  39. J. Vidal, G. Palacios, R. Mosseri, Phys. Rev. A 69, 022107 (2004)

    Article  ADS  Google Scholar 

  40. H.T. Quan, Z.D. Wang, C.P. Sun, Phys. Rev. A 76, 012104 (2007)

    Article  ADS  Google Scholar 

  41. R. Orus, S. Dusuel, J. Vidal, Phys. Rev. Lett. 101, 025701 (2008)

    Article  ADS  Google Scholar 

  42. Q. Wang, P. Wang, Y.B. Yang, W.G. Wang, Phys. Rev. A 91, 042102 (2015)

    Article  ADS  Google Scholar 

  43. S. Dusuel, J. Vidal, Phys. Rev. B 71, 224420 (2005)

    Article  ADS  Google Scholar 

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

  45. H.P. Breuer, E.M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  46. S. Wißmann, A. Karlsson, E.M. Laine, J. Piilo, H.P. Breuer, Phys. Rev. A 86, 062108 (2012)

    Article  ADS  Google Scholar 

  47. T.J.G. Apollaro, C. Di Franco, F. Plastina, M. Paternostro, Phys. Rev. A 83, 032103 (2011)

    Article  ADS  Google Scholar 

  48. J. Jing, L.-A. Wu, A. del Campo, arXiv:1510.01106

  49. B. Simon, Trace Ideals and Their Applications (Springer, Berlin, 2005)

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Authors and Affiliations

  1. School of Physics, Beijing Institute of Technology, 100081, Beijing, P.R. China

    Lu Hou, Bin Shao & Jian Zou

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  1. Lu Hou
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  2. Bin Shao
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  3. Jian Zou
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Correspondence to Bin Shao.

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Hou, L., Shao, B. & Zou, J. Quantum speed limit for a central system in Lipkin-Meshkov-Glick bath. Eur. Phys. J. D 70, 35 (2016). https://doi.org/10.1140/epjd/e2016-60600-5

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  • DOI: https://doi.org/10.1140/epjd/e2016-60600-5

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