Skip to main content
SpringerLink
Log in

BCS Effect on Quantum Correlation and Tripartite Quantum Entanglement in Spinless Gapless Tomonaga-Luttinger Liquid and Cuprate Superconducting Nanowire

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

It has been known that quantum information offers powerful instruments to investigate the properties of many-body systems. In this framework, we touched two particular aspect of this activity, namely the quantum entanglement and discord to compare the properties of gapless Tomonaga-Luttinger Liquid (TLL) model and the effect of BCS coupling in spinless fermions of TLL as a cuprate superconducting nanowire. Using two-fermion space-spin density matrix, we investigate quantum correlation of these cases via bipartite and tripartite entanglement, as well as quantum discord. The relations of concurrence (as a measure of quantum entanglement), the lower bound of the generalized robustness of tripartite entanglement and quantum discord in terms of the relative distance between fermions and the coupling parameter were accordingly obtained. The relationship between the compressibility as a physical property of system and quantum correlations has also been studied.

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
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Damascelli, A., Hussain, Z., Shen, Z.X.: Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473–541 (2003)

    Article  ADS  Google Scholar 

  2. M. Fisher, arXiv:cond-mat/9806164 (1998)

  3. Moreno, M., Ford, C.J.B., Jin, Y., Griffiths, J.P., Farrer, I., Jones, G.A.C., Ritchie, D.A., Tsyplyatyev, O., Schofield, A.J.: Nonlinear spectra of spinons and holons in short GaAs quantum wires. Nat. Commun. 7, 12784 (2016)

    Article  ADS  Google Scholar 

  4. Bellucci, S., Onorato, P.: Eur. Phys. J. B. 45, 87 (2005)

    Article  ADS  Google Scholar 

  5. Hausler, W., Kecke, L., MacDonald, A.H.: Tomonaga-Luttinger parameters for quantum wires. Phys. Rev. B. 65, 085104 (2002)

    Article  ADS  Google Scholar 

  6. Finkel’stein, A.M., Larkin, A.I.: Two coupled chains with Tomonaga-Luttinger interactions. Phys. Rev. B. 47, 10461–10473 (1993)

    Article  ADS  Google Scholar 

  7. Tomonaga, S.: Remarks on Bloch’s method of sound waves applied to Many-Fermion Problems. Prog. Theor. Phys. 5, 544–569 (1950)

    Article  ADS  MathSciNet  Google Scholar 

  8. Luttinger, J.M.: An exactly soluble model of a Many‐Fermion System. J. Math. Phys. 4, 1154–1162 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  9. Blochl, P.E., Pruschke, T., Potthof, M.: Phys. Rev. B. 88, 205139 (2013)

    Article  ADS  Google Scholar 

  10. Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature. 404, 247–255 (2000)

    Article  ADS  Google Scholar 

  11. Lee, J.W., Oh, S., Kim, J.: Phys. Lett. A. 363, 5 (2005)

    Google Scholar 

  12. Yonac, M., Yu, T., Eberly, J.H.: J. Phys. B. 39, 15 (2006)

    Article  Google Scholar 

  13. 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 

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

    Article  ADS  MathSciNet  Google Scholar 

  15. Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  16. Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A., Wootters, W.K.: Quantum nonlocality without entanglement. Phys. Rev. A. 59, 1070–1091 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  17. Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sen, A., Sen, U., Synak-Radtke, B.: Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A. 71, 062307 (2005)

    Article  ADS  Google Scholar 

  18. Niset, J., Cerf, N.J.: Multipartite nonlocality without entanglement in many dimensions. Phys. Rev. A. 74, 052103 (2006)

    Article  ADS  Google Scholar 

  19. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  Google Scholar 

  20. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A. 34, 6899–6905 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  21. Zhang, J.S., Chen, A.X.: Quant. Phys. Lett. 1, 69 (2012)

    ADS  Google Scholar 

  22. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A. 77, 042303 (2008)

    Article  ADS  Google Scholar 

  23. Li, N., Luo, S.: Phys. Rev. A. 76, 032327 (2007) S. Luo, ibid 77, 022301 (2008)

    Article  ADS  Google Scholar 

  24. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubitXstates. Phys. Rev. A. 81, 042105 (2010)

    Article  ADS  Google Scholar 

  25. Girolami, D., Adesso, G.: Quantum discord for general two-qubit states: analytical progress. Phys. Rev. A. 83, 052108 (2011)

    Article  ADS  Google Scholar 

  26. Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubitXstates. Phys. Rev. A. 84, 042313 (2011)

    Article  ADS  Google Scholar 

  27. Afzali, R., Ebrahimian, N., Eghbalifar, B.: Quantum information aspects on bulk and nano interacting Fermi system: A spin-space density matrix approach. Phys. Lett. A. 380, 3394–3403 (2016)

    Article  ADS  Google Scholar 

  28. Afzali, R., Fahimi, S., Dehghan, M.: Quantum entanglement and correlation lengths of a S-wave superconductors in the presence of a weak constant external potential. Int. J. Theor. Phys. 56, 1565–1576 (2017)

    Article  Google Scholar 

  29. Eneias, R., Ferraz, A.: BCS coupling in a 1D Luttinger liquid. New J. Phys. 17, 123006 (2015)

    Article  ADS  Google Scholar 

  30. Witten, E.: Nucl. Phys. B. 145, 110 (1978)

    Article  ADS  Google Scholar 

  31. Coleman, S.: Phys. Rev. D. 11, 2088 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  32. Solyom, J.: The Fermi gas model of one-dimensional conductors. Adv. Phys. 28, 201–303 (1979)

    Article  ADS  Google Scholar 

  33. Voit, J.: Prog. Phys. 58, 9 (1995)

    Article  Google Scholar 

  34. Oh, S., Kim, J.: Entanglement of electron spins in superconductors. Phys. Rev. B. 71, 144523 (2005)

    Article  ADS  Google Scholar 

  35. Oh, S., Kim, J.: Entanglement of electron spins of noninteracting electron gases. Phys. Rev. A. 69, 054305 (2004)

    Article  ADS  Google Scholar 

  36. Vedral, V.: Central Eur. J. Phys. 1, 289 (2003)

    ADS  Google Scholar 

  37. Lunkes, C., Brukner, C., Vedral, V.: Natural multiparticle entanglement in a Fermi gas. Phys. Rev. Lett. 95, 030503 (2005)

    Article  ADS  Google Scholar 

  38. Clark, J.W., Habibian, H., Mandilara, A.D., Ristig, M.L.: Found Phys. 40, 1200 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  39. Vértesi, T.: Genuine tripartite entanglement in the noninteracting Fermi gas. Phys. Rev. A. 75, 042330 (2007)

    Article  ADS  Google Scholar 

  40. Cavalcanti, D., Cunha, M.O.T.: Estimating entanglement of unknown states. Appl. Phys. Lett. 89, 084102 (2006)

    Article  ADS  Google Scholar 

  41. Eisert, J., Brandão, F.G.S.L., Audenart, K.M.R.: New J. Phys. 9, 46 (2007)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the helpful discussion with Dr. Alvaro Ferraz.

Author information

Authors and Affiliations

  1. Department of Physics, K. N. Toosi University of Technology, Tehran, 15875-4416, Iran

    M. R. Montazeri & R. Afzali

Authors
  1. M. R. Montazeri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Afzali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Afzali.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Montazeri, M.R., Afzali, R. BCS Effect on Quantum Correlation and Tripartite Quantum Entanglement in Spinless Gapless Tomonaga-Luttinger Liquid and Cuprate Superconducting Nanowire. Int J Theor Phys 60, 3797–3814 (2021). https://doi.org/10.1007/s10773-021-04928-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-021-04928-4

Keywords

Search

Navigation