Skip to main content
SpringerLink
Log in

Density matrix spectra and order parameters in the 1D extended Hubbard model

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Without any knowledge of the symmetry existing in a system, we derive the exact forms of the order parameters which show long-range correlations in the ground state of the one-dimensional (1D) extended Hubbard model using a quantum information approach. Our work demonstrates that the quantum information approach can help us to find the explicit form of the order parameter, which could not be derived systematically via traditional methods in the condensed matter theory.

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

Similar content being viewed by others

References

  1. G.D. Mahan, Many Particle Physics (Kluwer Academic/Plenum Publishers, New York, 2000)

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

  3. S. Furukawa, G. Misguich, M. Oshikawa, Phys. Rev. Lett. 96, 047211 (2006)

    Article  ADS  Google Scholar 

  4. C.L. Henley, H.J. Changlani, J. Stat. Mech. 2014, P11002 (2014)

    Article  MathSciNet  Google Scholar 

  5. S.-A. Cheong, C.L. Henley, Phys. Rev. B 79, 212402 (2009)

    Article  ADS  Google Scholar 

  6. S.J. Gu, W.C. Yu, H.Q. Lin, Ann. Phys. 336, 118 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  7. G.W. Hayden, Z.G. Soos, Phys. Rev. B 38, 6075 (1988)

    Article  ADS  Google Scholar 

  8. D.K. Campbell, T.A. DeGrand, S. Mazumdar, Phys. Rev. Lett. 52, 1717 (1984)

    Article  ADS  Google Scholar 

  9. H.J. Schulz, Phys. Rev. Lett. 64, 2831 (1990)

    Article  ADS  Google Scholar 

  10. M.M. Wolf, F. Verstraete, M.B. Hastings, J.I. Cirac, Phys. Rev. Lett. 100, 070502 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  11. S.J. Gu, C.P. Sun, H.Q. Lin, J. Phys. A 41, 025002 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  12. V.J. Emery, in Highly Conducting One Dimensional Solids, edited by J.T. Devreese et al. (Plenum, New York, 1979), pp. 247–303

  13. J. Solyom, Adv. Phys. 28, 201 (1979)

    Article  ADS  Google Scholar 

  14. V.J. Emery, Phys. Rev. B 14, 2989 (1976)

    Article  ADS  Google Scholar 

  15. M. Fowler, Phys. Rev. B 17, 2989 (1978)

    Article  ADS  Google Scholar 

  16. G.S. Tian, Phys. Rev. B 45, 3145 (1992)

    Article  ADS  Google Scholar 

  17. H.Q. Lin, E.R. Gagliano, D.K. Campbell, E.H. Fradkin, J.E. Gubernatis, in The Hubbard Model: Its Physics and Mathematical Physics, edited by D. Baeriswyl et al. (Plenum, New York, 1995), pp. 315–327

  18. H.Q. Lin, D.K. Campbell, R.T. Clay, Chin. J. Phys. 38, 1 (2000)

    MathSciNet  Google Scholar 

  19. J.E. Hirsch, Phys. Rev. Lett. 53, 2327 (1984)

    Article  ADS  Google Scholar 

  20. S.J. Gu, S.S. Deng, Y.Q. Li, H.Q. Lin, Phys. Rev. Lett. 93, 086402 (2004)

    Article  ADS  Google Scholar 

  21. S.S. Deng, S.J. Gu, H.Q. Lin, Phys. Rev. B 74, 045103 (2006)

    Article  ADS  Google Scholar 

  22. M. Nakamura, J. Phys. Soc. Jpn 68, 3123 (1999)

    Article  ADS  Google Scholar 

  23. M. Nakamura, Phys. Rev. B 61, 16377 (2000)

    Article  ADS  Google Scholar 

  24. E. Jeckelmann, Phys. Rev. Lett. 89, 236401 (2002)

    Article  ADS  Google Scholar 

  25. E. Jeckelmann, Phys. Rev. Lett. 91, 089702 (2003)

    Article  ADS  Google Scholar 

  26. P. Sengupta, A.W. Sandvik, D.K. Campbell, Phys. Rev. B 65, 155113 (2002)

    Article  ADS  Google Scholar 

  27. A.W. Sandvik, L. Balents, D.K. Campbell, Phys. Rev. Lett. 92, 236401 (2004)

    Article  ADS  Google Scholar 

  28. Y.Z. Zhang, Phys. Rev. Lett. 92, 246404 (2004)

    Article  ADS  Google Scholar 

  29. S. Ejima, S. Nishimoto, Phys. Rev. Lett. 99, 216403 (2007)

    Article  ADS  Google Scholar 

  30. M. Tsuchiizu, A. Furusaki, Phys. Rev. Lett. 88, 056402 (2002)

    Article  ADS  Google Scholar 

  31. M. Tsuchiizu, A. Furusaki, Phys. Rev. B 69, 035103 (2004)

    Article  ADS  Google Scholar 

  32. C. Mund, O. Legeza, R.M. Noack, Phys. Rev. B 79, 245130 (2009)

    Article  ADS  Google Scholar 

  33. G.-H. Liu, C.-H. Wang, Commun. Theor. Phys. 55, 702 (2011)

    Article  ADS  Google Scholar 

  34. Y.C. Li, Z.G. Yuan, Phys. Lett. A 380, 272 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  35. J. Hubbard, Proc. Roy. Soc. A 276, 238 (1963)

    Article  ADS  Google Scholar 

  36. M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963)

    Article  ADS  Google Scholar 

  37. J. Kanamori, Prog. Theor. Phys. 30, 275 (1963)

    Article  ADS  Google Scholar 

  38. P.D. Sacramento, Y.C. Li, S.J. Gu, J.M.P. Carmelo, Eur. Phys. J. B 86, 507 (2013)

    Article  ADS  Google Scholar 

  39. G. Misguich, C. Lhuillier, in Frustrated spin systems, edited by H.T. Diep (World-Scientific, Singapore, 2005)

  40. T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  41. A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416, 608 (2002)

    Article  ADS  Google Scholar 

  42. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. P. Zanardi, N. Paunković, Phys. Rev. E 74, 031123 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  45. S.J. Gu, Int. J. Mod. Phys. B 24, 4371 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and ITP, The Chinese University of Hong Kong, Hong Kong, P.R. China

    Wing Chi Yu & Shi-Jian Gu

  2. Beijing Computational Science Research Center, Beijing, 100084, P.R. China

    Hai-Qing Lin

Authors
  1. Wing Chi Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shi-Jian Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hai-Qing Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wing Chi Yu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, W., Gu, SJ. & Lin, HQ. Density matrix spectra and order parameters in the 1D extended Hubbard model. Eur. Phys. J. B 89, 212 (2016). https://doi.org/10.1140/epjb/e2016-70361-6

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2016-70361-6

Keywords

Search

Navigation