Skip to main content
SpringerLink
Log in

Exploration of quantum phases transition in the XXZ model with Dzyaloshinskii–Moriya interaction using trance distance discord

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In the paper, we researched the quantum phase transition (QPT) in the anisotropic spin XXZ model by exploiting the quantum renormalization group (QRG) method. The innovation point is that we adopt a new approach called trace distance discord to indicate the quantum correlation of the system. QPT after several iterations of renormalization in current system has been observed. Consequently, it opened the possibility of investigation of QPR in the geometric discord territory. While the anisotropy suppresses the correlation due to favoring of the alignment of spins, the DM interaction restores the spoiled correlation via creation of the quantum fluctuations. We also apply quantum renormalization group method to probe the thermodynamic limit of the model and emerging of nonanalytic behavior of the correlation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Bell, J.S.: Physics (Long Island City, N.Y.) 1, 195 (1964)

    Google Scholar 

  2. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Communication. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  3. Sachdev, S.: Quantum Phase Transitions. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  4. Osterloh, A., Amico, L., Falci, G., Rosario, F.: Scaling of entanglement close to a quantum phase transition. Nature (London) 416, 608 (2002)

    Article  ADS  Google Scholar 

  5. Wu, L.A., Sarandy, M.S., Lidar, D.A.: Quantum phase transitions and bipartite entanglement. Phys. Rev. Lett. 93, 250404 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  6. Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90, 227902 (2003)

    Article  ADS  Google Scholar 

  7. Vidal, J., Palacios, G., Mosseri, R.: Entanglement in a second-order quantum phase transition. Phys. Rev. A 69, 022107 (2004)

    Article  ADS  Google Scholar 

  8. Osborne, T.J., Nielsen, M.A.: Entanglement in a simple quantum phase transition. Phys. Rev. A 66, 032110 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  9. Bose, I., Chattopadhyay, E.: Macroscopic entanglement jumps in model spin systems. Phys. Rev. A 66, 062320 (2002)

    Article  ADS  Google Scholar 

  10. Verstraete, F., Popp, M., Cirac, J.I.: Entanglement versus correlations in spin systems. Phys. Rev. Lett. 92, 027901 (2004)

    Article  ADS  Google Scholar 

  11. Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Gu, S.-J., Deng, S.-S., Li, Y.-Q., Lin, H.-Q.: Entanglement and quantum phase transition in the extended Hubbard model. Phys. Rev. Lett. 93, 086402 (2004)

    Article  ADS  Google Scholar 

  13. Anfossi, A., Giorda, P., Montorsi, A.: Entanglement in extended Hubbard models and quantum phase transitions. Phys. Rev. B 75, 165106 (2007)

    Article  ADS  Google Scholar 

  14. Xu, S., Song, X.K., Ye, L.: Measurement-induced disturbance and negativity in mixed-spin XXZ model. Quant. Inf. Process 13, 1013–1024 (2014)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Song, X.K., Wu, T., Ye, L.: The monogamy relation and quantum phase transition in one-dimensional anisotropic XXZ model. Quant. Inf. Process 12, 3305–3317 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Debarba, T., Maciel, T.O., Vianna, R.: O: Witnessed entanglement and the geometric measure of quantum discord. Phys. Rev. A 86, 024302 (2012) Debarba. T, Maciel. T. O ., Vianna. R .O 2012 arXiv:1207.1298v3 (erratum)

  17. Rana, S., Parashar, P.: Comment on “Witnessed entanglement and the geometric measure of quantum discord”. Phys. Rev. A 87, 016301 (2013)

    Article  ADS  Google Scholar 

  18. Nakano, T., Piani, M., Adesso, G.: Negativity of quantumness and its interpretations. Phys. Rev. A 88, 012117 (2013)

    Article  ADS  Google Scholar 

  19. Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten 1-norm. Phys. Rev. A 87, 064101 (2013)

    Article  ADS  Google Scholar 

  20. Montealegre, J.D., Paula, F.M., Saguia, A., Sarandy, M.S.: One-norm geometric quantum discord under decoherence. Phys. Rev. A 87, 042115 (2013)

    Article  ADS  Google Scholar 

  21. Gilchrist, A., Langford, N.K., Nielsen, M.A.: Distance measures to compare real and ideal quantum processes. Phys. Rev. A 71, 062310 (2005)

    Article  ADS  Google Scholar 

  22. Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120 (1998)

    Article  ADS  Google Scholar 

  23. Raussendorf, R., Briegel, H. J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2000)

  24. Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91 (1960)

    Article  ADS  Google Scholar 

  25. Mart’ın-Delgado, M.A., Sierra, G.: Analytic formulations of the density matrix renormalization group. Int. J. Mod. Phys. A 11, 3145 (1996)

    Article  ADS  Google Scholar 

  26. Langari, A.: Phase diagram of the antiferromagnetic XXZ model in the presence of an external magnetic field. Phys. Rev. B 58, 14467 (1998)

    Article  ADS  Google Scholar 

  27. Jafari, R., Langari, A.: Phase Diagram of spin 1/2 XXZ Model With Dzyaloshinskii–Moriya Interaction. e-print arXiv:0812.1862

  28. Ciccarello, F., Tufarelli, T., Giovannetti, V.: Toward computability of trace distance discord. New J. Phys. 16, 013038 (2014)

    Article  ADS  Google Scholar 

  29. Kargarian, M., Jafari, R., Langari, A.: Renormalization of entanglement in the anisotropic Heisenberg (XXZ) model. Phys. Rev. A 77, 032346 (2008)

    Article  ADS  Google Scholar 

  30. Dzyaloshinsky, I.: A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241 (1958)

    Article  ADS  Google Scholar 

  31. Alcaraz, F.C., Wreszinski, W.F.: The Heisenberg XXZ Hamiltonian with Dzyaloshinsky–Moriya interactions. J. Stat. Phys. 58, 45 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  32. Aristov, D.N., Maleyev, S.V.: Spin chirality induced by the Dzyaloshinskii–Moriya interaction and polarized neutron scattering. Phys. Rev. B 62, R751 (2000)

    Article  ADS  Google Scholar 

  33. Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Science Foundation of China under Grants No. 11074002 and No. 61275119, the Doctoral Foundation of the Ministry of Education of China under Grant No. 20103401110003, the Personal Development Foundation of Anhui Province (2008Z018), and also by the Natural Science Research Project of Education Department of Anhui Province of China (Grant No. KJ2013A205).

Author information

Authors and Affiliations

  1. School of Physics and Material Science, Anhui University, Hefei, 230601, China

    Ren-jie Zhang, Shuai Xu, Jia-dong Shi, Wen-chao Ma & Liu Ye

Authors
  1. Ren-jie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuai Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jia-dong Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wen-chao Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Liu Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liu Ye.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Rj., Xu, S., Shi, Jd. et al. Exploration of quantum phases transition in the XXZ model with Dzyaloshinskii–Moriya interaction using trance distance discord. Quantum Inf Process 14, 4077–4088 (2015). https://doi.org/10.1007/s11128-015-1102-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-1102-1

Keywords

Search

Navigation