Skip to main content
SpringerLink
Log in

Ordered phases of XXZ-symmetric spin-1/2 zigzag ladder

  • Published:
The European Physical Journal B - Condensed Matter and Complex Systems Aims and scope Submit manuscript

Abstract.

Using bosonization approach, we derive an effective low-energy theory for XXZ-symmetric spin-1/2 zigzag ladders and discuss its phase diagram by a variational approach. A spin nematic phase emerges in a wide part of the phase diagram, either critical or massive. Possible crossovers between the spontaneously dimerized and spin nematic phases are discussed, and the topological excitations in all phases identified.

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. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 1999)

  2. P. Lecheminant, arXiv:cond-mat/0306520

  3. R. Coldea, D.A. Tennant, R.A. Cowley, D.F. McMorrow, B. Dorner, Z. Tylczynski, Phys. Rev. Lett. 79, 151 (1997); R. Coldea, D.A. Tennant, A.M. Tsvelik, Z. Tylczynski, Phys. Rev. Lett. 86, 1335 (2001); R. Coldea, D.A. Tennant, Z. Tylczynski, Phys. Rev. B 68, 13424 (2003)

    Article  Google Scholar 

  4. F.D.M. Haldane, Phys. Rev. B 25, 4925 (1982)

    Article  Google Scholar 

  5. S. Eggert, Phys. Rev. B 54, 961 (1996)

    Article  Google Scholar 

  6. K.Okamoto, K. Nomura, Phys. Lett. A 169, 433 (1992)

    Article  Google Scholar 

  7. S.R. White, I. Affleck, Phys. Rev. B 54, 9862 (1996)

    Article  Google Scholar 

  8. C.K. Majumdar, D.K. Ghosh, J. Math. Phys 10, 1388 (1969)

    Article  Google Scholar 

  9. A.A. Aligia, C.D. Batista, F.H.L. Essler, Phys. Rev. B 62, 3259 (2000)

    Article  Google Scholar 

  10. A.A. Nersesyan, A.O. Gogolin, F.H.L. Essler, Phys. Rev. Lett. 81, 910 (1998)

    Article  Google Scholar 

  11. T. Hikihara, M. Kaburagi, H. Kawamura, Phys. Rev. B 63, 174430 (2001)

    Article  Google Scholar 

  12. T. Hikihara, M. Kaburagi, H. Kawamura, Prog. Theor. Phys. Suppl. 145, 58 (2002)

    Google Scholar 

  13. P.D. Sacramento, V.R. Vieira, J. Phys.: Condens. Matter 14, 591 (2002)

    Article  Google Scholar 

  14. V.R. Vieira, N. Guihery, J.P. Rodriguez, P.D. Sacramento, Phys. Rev. B 63, 224417 (2001)

    Article  Google Scholar 

  15. H. Fukushima, H. Kikuchi, M. Chiba, Y. Fujii, Y. Yamamoto, H. Hori, Prog. Theor. Phys. Suppl. 145, 72 (2002)

    Google Scholar 

  16. P. Lecheminant, T. Jolicoeur, P. Azaria, Phys. Rev. B 63, 174426 (2001)

    Article  Google Scholar 

  17. A.K. Kolezhuk, Phys. Rev. B 62, R6057 (2000)

  18. A. Luther, I. Peschel, Phys. Rev. B 12, 3908 (1975)

    Article  Google Scholar 

  19. A.O. Gogolin, A.A. Nersesyan, A.M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge Univ. Press, Cambridge, 1999)

  20. D.C. Cabra, A. Honecker, P. Pujol, Eur. Phys. J. B 13, 55 (2000)

    Google Scholar 

  21. D. Shelton, A.A. Nersesyan, A.M. Tsvelik, Phys. Rev B 53, 8521 (1996)

    Article  Google Scholar 

  22. D. Allen, D. Senechal, Phys. Rev. B 55, 299 (1997)

    Article  Google Scholar 

  23. D. Allen, F.H.L. Essler, A.A. Nersesyan, Phys. Rev. B 61, 8871 (2000)

    Article  Google Scholar 

  24. It should be remembered that it is only at the SU(2) point that all three components of the vector current satisfy the SU(2)1 Kac-Moody algebra. In the XXZ case (\(\Delta < 1\)) J x R,L and J y R,L acquire anomalous dimensions, and only J z R,L remain as the generators of U(1) R,L .

  25. S. Lukyanov, A.B. Zamolodchikov, Nucl. Phys. B 493, 571 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  26. S. Lukyanov, Mod. Phys. Lett. A 12, 2543 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  27. S. Coleman, Phys. Rev. D 11, 2088 (1975). For an equivalent Self-Consistent Harmonic Approximation see Y. Suzumura, Prog. Theor. Phys. 61, 1 (1979)

    Article  Google Scholar 

  28. Z. Weihong, V. Kotov, J. Oitmaa, Phys. Rev. B 57, 11 439 (1998); X. Wang, Mod. Phys. Lett. B 14, 327 (2000) A.K. Kolezhuk, H.-J. Mikeska, Int. J. Mod. Phys. B 5, 2325 (1998)

    Article  Google Scholar 

  29. Massive spinons carrying fractional quantum numbers have been recently shown to persist in a higher-dimensional version of the model (26); see A.A. Nersesyan, A.M. Tsvelik, Phys. Rev. B 67, 024422 (2003)

    Article  Google Scholar 

  30. G. Delfino, G. Mussardo, Nucl. Phys. B 516, 675 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  31. M. Fabrizio, A.O. Gogolin, A.A. Nersesyan, Nucl. Phys. B 580, 647 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  32. A.M. Tsvelik, Nucl. Phys. B 612, 479 (2001)

    Article  MATH  Google Scholar 

  33. P. Di Francesco, P. Mathieu, D. Senechal, Conformal Field Theory (Springer-Verlag, NY, 1996)

Download references

Author information

Authors and Affiliations

  1. International School for Advanced Studies, Via Beirut 4, 34014, Trieste, Italy

    M. Zarea & M. Fabrizio

  2. The Abdus Salam International Centre for Theoretical Physics, P.O. Box 586, 34100, Trieste, Italy

    A. A. Nersesyan

  3. The Andronikashvili Institute of Physics, Tamarashvili 6, 380077, Tbilisi, Georgia

    A. A. Nersesyan

Authors
  1. M. Zarea
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Fabrizio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. A. Nersesyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Fabrizio.

Additional information

Received: 14 August 2004, Published online: 29 June 2004

PACS:

75.10.Pq Spin chain models - 75.40.-s Critical-point effects, specific heats, short-range order - 75.30.Gw Magnetic anisotropy - 71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zarea, M., Fabrizio, M. & Nersesyan, A.A. Ordered phases of XXZ-symmetric spin-1/2 zigzag ladder. Eur. Phys. J. B 39, 155–168 (2004). https://doi.org/10.1140/epjb/e2004-00180-3

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2004-00180-3

Keywords

Search

Navigation