International Journal of Theoretical Physics

, Volume 57, Issue 2, pp 363–370 | Cite as

One-Way Deficit and Quantum Phase Transitions in XX Model



Quantum correlations including entanglement and quantum discord have drawn much attention in characterizing quantum phase transitions. Quantum deficit originates in questions regarding work extraction from quantum systems coupled to a heat bath (Oppenheim et al. Phys. Rev. Lett. 89, 180402, 2002). It links quantum thermodynamics with quantum correlations and provides a new standpoint for understanding quantum non-locality. In this paper, we evaluate the one-way deficit of two adjacent spins in the bulk for the XX model. In the thermodynamic limit, the XX model undergoes a first order transition from fully polarized to a critical phase with quasi-long-range order with decrease of quantum parameter. We find that the one-way deficit becomes nonzero after the critical point. Therefore, the one-way deficit characterizes the quantum phase transition in the XX model.


One way deficit Quantum phase transition XX Model 



We are thankful to Jin-Jun Chen for fruitful discussions. This work was supported by the Science and Technology Research Plan Project of the Department of Education of Jilin Province in the Twelfth Five-Year Plan, the National Natural Science Foundation of China under grant Nos. 11175248, 11275131, 11305105.


  1. 1.
    Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Nature (London) 464, 45 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Rev. Mod. Phys. 80, 517 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    Wu, L.A., Sarandy, M.S., Lidar, D.A.: Phys. Rev. Lett. 93, 250404 (2004)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Orús, R., Wei, T.C.: Phys. Rev. B 82, 155120 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    Dillenschneider, R.: Phys. Rev. B 78, 224413 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    Amico, L., Patan, D.: EPL (Europhys. Lett.) 77, 17001 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Rev. Mod. Phys. 80, 517 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    Sarandy, M.S.: Phys. Rev. A 80, 022108 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    Werlang, T., Trippe, C., Ribeiro, G.A.P., Rigolin, G.: Phys. Rev. Lett. 105, 095702 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Cui, J., Cao, J.-P., Fan, H.: Phys. Rev. A 85, 022338 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    Cui, J., Gu, M., Kwek, L.C., Santos, M.F., Fan, H., Vedral, V.: Nat. Commun. 3, 812 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    Cui, J., Amico, L., Fan, H., Gu, M., Hamma, A., Vedral, V.: Phys. Rev. B 88, 125117 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    Franchini, F., Cui, J., Amico, L., Fan, H., Gu, M., Korepin, V., Kwek, L.C., Vedral, V.: Phys. Rev. X 4, 041028 (2014)Google Scholar
  14. 14.
    Oppenheim, J., Horodecki, M., Horodecki, P., Horodecki, R.: Phys. Rev. Lett. 89, 180402 (2002)ADSCrossRefGoogle Scholar
  15. 15.
    Horodecki, M., Horodecki, K., Horodecki, P., Horodecki, R., Oppenheim, J., Sen(De), A., Sen, U.: Phys. Rev. Lett. 90, 100402 (2003)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: Rev. Mod. Phys. 84, 1655 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sen(De), A., Sen, U., Synak, B.: Phys. Rev. A 71, 062307 (2005)ADSCrossRefGoogle Scholar
  18. 18.
    Horodecki, M., Horodecki, P., Oppenheim, J.: Phys. Rev. A 67, 062104 (2003)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Streltsov, A., Kampermann, H., Bruß, D.: Phys. Rev. Lett. 108, 250501 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    Chuan, T.K., Maillard, J., Modi, K., Paterek, T., Paternostro, M., Piani, M.: Phys. Rev. Lett. 109, 070501 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    Streltsov, A., Kampermann, H., Bruß, D.: Phys. Rev. Lett. 106, 160401 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    De Pasquale, A., Costantini, G., Facchi, P., Florio, G., Pascazio, S., Yuasa, K.: Eur. Phys. J. Spec. Top. 160, 127 (2008)CrossRefGoogle Scholar
  23. 23.
    Son, W., Amico, L., Plastina, F., Vedral, V.: Phys. Rev. A 79, 022302 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    Chen, J.-J., Cui, J., Fan, H.: arXiv:1509.03576v1
  25. 25.
    Luo, S.: Phys. Rev. A 77, 042303 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.College of MathematicsTonghua Normal UniversityTonghuaPeople’s Republic of China
  2. 2.Institute of PhysicsChinese Academy of SciencesBeijingPeople’s Republic of China

Personalised recommendations