Markovian evolution of classical and quantum correlations in transverse-field XY model

Regular Article

Abstract

The transverse-field XY model in one dimension is a well-known spin model for which the ground state properties and excitation spectrum are known exactly. The model has an interesting phase diagram describing quantum phase transitions (QPTs) belonging to two different universality classes. These are the transverse-field Ising model and the XX model universality classes with both the models being special cases of the transverse-field XY model. In recent years, quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity have been shown to provide signatures of QPTs. Another interesting issue is that of decoherence to which a quantum system is subjected due to its interaction, represented by a quantum channel, with an environment. In this paper, we determine the dynamics of different types of correlations present in a quantum system, namely, the mutual information I(ρ AB ), the classical correlations C(ρ AB ) and the quantum correlations Q(ρ AB ), as measured by the quantum discord, in a two-qubit state. The density matrix of this state is given by the nearest-neighbour reduced density matrix obtained from the ground state of the transverse-field XY model in 1d. We assume Markovian dynamics for the time-evolution due to system-environment interactions. The quantum channels considered include the bit-flip, bit-phase-flip and phase-flip channels. Two different types of dynamics are identified for the channels in one of which the quantum correlations are greater in magnitude than the classical correlations in a finite time interval. The origins of the different types of dynamics are further explained. For the different channels, appropriate quantities associated with the dynamics of the correlations are identified which provide signatures of QPTs. We also report results for further-neighbour two-qubit states and finite temperatures.

Keywords

Solid State and Materials 

References

  1. 1.
    E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 60, 407 (1961)MathSciNetADSGoogle Scholar
  2. 2.
    E. Barouch, B. McCoy, Phys. Rev. A 3, 786 (1971)ADSCrossRefGoogle Scholar
  3. 3.
    P. Pfeuty, Ann. Phys. 57, 79 (1970)ADSCrossRefGoogle Scholar
  4. 4.
    M. Zhong, P. Tong, J. Phys. A Math. Theor. 43, 505302 (2010) MathSciNetCrossRefGoogle Scholar
  5. 5.
    A. Dutta, U. Divakaran, B.K. Chakrabarti, T.F. Rosenbaum, G. Aeppli, arXiv:1012.0653v1 [cond-mat.stat-mech]Google Scholar
  6. 6.
    J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002) MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416, 608 (2002) ADSCrossRefGoogle Scholar
  8. 8.
    L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)MathSciNetADSCrossRefMATHGoogle Scholar
  9. 9.
    M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, U. Sen, Adv. Phys. 56, 243 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    M.S. Sarandy, Phys. Rev. A 80, 022108 (2009) ADSCrossRefGoogle Scholar
  11. 11.
    R. Dillenschneider, Phys. Rev. B 78, 224413 (2008) ADSCrossRefGoogle Scholar
  12. 12.
    T. Werlang, G.A.P. Ribeiro, G. Rigolin, Phys. Rev. A 83, 062334 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    P. Zanardi, N. Paunković, Phys. Rev. E 74, 031123 (2006) MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    I. Bose, E. Chattopadhyay, Phys. Rev. A 66, 062320 (2002) ADSCrossRefGoogle Scholar
  15. 15.
    L.-A. Wu, M.S. Sarandy, D.A. Lidar, Phys. Rev. Lett. 93, 250403 (2004) MathSciNetCrossRefGoogle Scholar
  16. 16.
    H. Ollivier, W.H. Zurek, Phys. Rev. Lett. 88, 017901 (2001) ADSCrossRefGoogle Scholar
  17. 17.
    L. Henderson, V. Vedral, J. Phys. A 34, 6899 (2001) MathSciNetADSCrossRefMATHGoogle Scholar
  18. 18.
    J. Maziero, T. Werlang, F.F. Fanchini, L.C. Céleri, R.M. Serra, Phys. Rev. A 81, 022116 (2010) ADSCrossRefGoogle Scholar
  19. 19.
    M.P. Almeida et al., Science 316, 579 (2007) ADSCrossRefGoogle Scholar
  20. 20.
    T. Werlang, S. Souza, F.F. Fanchini, C. Villas Boas, Phys. Rev. A 80, 024103 (2009) ADSCrossRefGoogle Scholar
  21. 21.
    J. Maziero, L.C. Céleri, R.M. Serra, V. Vedral, Phys. Rev. A 80, 044102 (2009) MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    L. Mazzola, J. Piilo, S. Maniscalco, Phys. Rev. Lett. 104, 200401 (2001) MathSciNetCrossRefGoogle Scholar
  23. 23.
    A.K. Pal, I. Bose, J. Phys. B At. Mol. Opt. Phys. 44, 045101 (2011) ADSCrossRefGoogle Scholar
  24. 24.
    A.K. Pal, I. Bose, Eur. Phys. J. B 85, 36 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    A. Ferraro, L. Aolita, D. Cavalcanti, F.M. Cucchietti, A. Acin, Phys. Rev. A 81, 052318 (2010) ADSCrossRefGoogle Scholar
  26. 26.
    J.-S. Xu, X.-Y. Xu, C.-F. Li, C.-J. Zhong, X.-B. Zoa, G.-C. Guo, Nat. Commun. 1, 7 (2010)Google Scholar
  27. 27.
    R. Auccaise et al., Phys. Rev. Lett. 107, 140403 (2011) ADSCrossRefGoogle Scholar
  28. 28.
    F.F. Fanchini, T. Werlang, C.A. Brasil, L.G.E. Arruda, A.O. Caldeira, Phys. Rev. A 81 052107 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000)Google Scholar
  30. 30.
    J. Maziero, H.C. Guzman, L.C. Céleri, M.S. Sarandy, R.M. Serra, Phys. Rev. A 82, 012106 (2010) ADSCrossRefGoogle Scholar
  31. 31.
    J. Maziero, L.C. Céleri, R.M. Serra, M.S. Sarandy, Phys. Lett. A 376, 1540 (2012)ADSCrossRefGoogle Scholar
  32. 32.
    T. Werlang, C. Trippe, G.A.P. Ribeiro, G. Rigolin, Phys. Rev. Lett. 105, 095702 (2010) ADSCrossRefGoogle Scholar
  33. 33.
    T. Werlang, G.A.P. Ribeiro, G. Rigolin (2012), arXiv:1205.1046v1[quant-ph]Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of PhysicsBose InstituteKolkataIndia

Personalised recommendations