The European Physical Journal B

, Volume 77, Issue 1, pp 139–146 | Cite as

Motion of bound domain walls in a spin ladder

Mesoscopic and Nanoscale Systems


The elementary excitation spectrum of the spin-\(\frac{1}{2}\) antiferromagnetic (AFM) Heisenberg chain is described in terms of a pair of freely propagating spinons. In the case of the Ising-like Heisenberg Hamiltonian spinons can be interpreted as domain walls (DWs) separating degenerate ground states. In dimension d > 1, the issue of spinons as elementary excitations is still unsettled. In this paper, we study two spin-\(\frac{1}{2}\) AFM ladder models in which the individual chains are described by the Ising-like Heisenberg Hamiltonian. The rung exchange interactions are assumed to be pure Ising-type in one case and Ising-like Heisenberg in the other. Using the low-energy effective Hamiltonian approach in a perturbative formulation, we show that the spinons are coupled in bound pairs. In the first model, the bound pairs are delocalized due to a four-spin ring exchange term in the effective Hamiltonian. The appropriate dynamic structure factor is calculated and the associated lineshape is found to be almost symmetric in contrast to the 1d case. In the case of the second model, the bound pair of spinons lowers its kinetic energy by propagating between chains. The results obtained are consistent with recent theoretical studies and experimental observations on ladder-like materials.


Exchange Interaction Elementary Excitation Dynamic Structure Factor Spin Pair Individual Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H.-J. Mikeska, A.K. Kolezhuk, in Quantum Magnetism, edited by U. Schollwöck, J. Richter, D.J.J. Farnell, R.F. Bishop (Springer, Berlin, 2004), p. 1 Google Scholar
  2. 2.
    J. Richter, J. Schulenberg, A. Honecker, in Quantum Magnetism, edited by U. Schollwöck, J. Richter, D.J.J. Farnell, R.F. Bishop (Springer, Berlin, 2004), p. 85 Google Scholar
  3. 3.
    I. Bose, Curr. Sci. 88, 62 (2005) Google Scholar
  4. 4.
    H. Bethe, Z. Phys. 71, 205 (1931) MATHADSCrossRefGoogle Scholar
  5. 5.
    B. Sutherland, in Beautiful Models (World Scientific, Singapore) Google Scholar
  6. 6.
    J. Villain, Physica B 79, 1 (1975) Google Scholar
  7. 7.
    N. Ishimura, H. Shiba, Prog. Theor. Phys. 63, 743 (1980) ADSCrossRefGoogle Scholar
  8. 8.
    S.E. Nagler, W.J.L. Buyers, R.L. Armstrong, B. Briat, Phys. Rev. B 28, 3873 (1983) ADSCrossRefGoogle Scholar
  9. 9.
    D.A. Tennant, T.G. Perring, R.A. Cowley, S.E. Nagler, Phys. Rev. Lett. 70, 4003 (1993) ADSCrossRefGoogle Scholar
  10. 10.
    P.W. Anderson, in The Theory of Superconductivity in the High-Tc Cuprates (Princeton University Press, Princeton, 1997) Google Scholar
  11. 11.
    S.A. Kivelson, D.S. Rokhsar, J.P. Sethna, Phys. Rev. B 35, 8865 (1987) ADSCrossRefGoogle Scholar
  12. 12.
    M. Levin, T. Senthil, Phys. Rev. B 70, 220403 (2004) ADSCrossRefGoogle Scholar
  13. 13.
    R. Coldea, D.A. Tennant, A.M. Tsvelik, Z. Tylczynski Phys. Rev. Lett. 86, 1335 (2001) ADSCrossRefGoogle Scholar
  14. 14.
    R. Coldea, D.A. Tennant, Z. Tylczynski, Phys. Rev. B 68, 134424 (2003) ADSCrossRefGoogle Scholar
  15. 15.
    M. Kohno, O.A. Starykh, L. Balents, Nat. Phys. 3, 790 (2007) CrossRefGoogle Scholar
  16. 16.
    D.G. Shelton, A.A. Nersesyan, A.M. Tsvelik, Phys. Rev. B 53, 8521 (1996) ADSCrossRefGoogle Scholar
  17. 17.
    M. Greiter, Phys. Rev. B 66, 054505 (2002) ADSCrossRefGoogle Scholar
  18. 18.
    C. Knetter, K.P. Schmidt, M. Grüninger, G.S. Uhrig, Phys. Rev. Lett. 87, 167204 (2001) ADSCrossRefGoogle Scholar
  19. 19.
    A.K. Kolezhuk, H.-J. Mikeska, Int. J. Mod. Phys. B 5, 2305 (1998) MathSciNetGoogle Scholar
  20. 20.
    J.-B. Fouet, F. Mila, D. Clarke, H. Youk, O. Tchernyshyov, P. Fendley, R.M. Noack, Phys. Rev. B 73, 214405 (2006) ADSCrossRefGoogle Scholar
  21. 21.
    B. Lake, A.M. Tsvelik, S. Notbohm, D.A. Tennant, T.G. Perring, M. Reehuis, C. Sekar, G. Krabbes, B. Büchner, Nat. Phys. 6, 50 (2009) CrossRefGoogle Scholar
  22. 22.
    F. Mila, Eur. Phys. J. B 6, 201 (1998) ADSCrossRefGoogle Scholar
  23. 23.
    K. Tandon, S. Lal, S.K. Pati, S. Ramasesha, D. Sen, Phys. Rev. B 59, 396 (1999) ADSCrossRefGoogle Scholar
  24. 24.
    N. Shannon, G. Misguich, K. Penc, Phys. Rev. B 69, 220403(R) (2004) ADSCrossRefGoogle Scholar
  25. 25.
    L. Balents, M.P.A. Fisher, S.M. Girvin, Phys. Rev. B 65, 224412 (2002) ADSCrossRefGoogle Scholar
  26. 26.
    I. Bose, S. Chatterjee, J. Phys. C 16, 947 (1983) ADSCrossRefGoogle Scholar
  27. 27.
    J.B. Torrance Jr., M. Tinkham, Phys. Rev. 187, 595 (1969) ADSCrossRefGoogle Scholar
  28. 28.
    T. Schneider, E. Stoll, Phys. Rev. Lett. 47, 377 (1981) ADSCrossRefGoogle Scholar
  29. 29.
    C.K. Majumdar, D.K. Ghosh, J. Math. Phys. 10, 1388 (1969) MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    F.D.M. Haldane, Phys. Rev. Lett. 60, 635 (1988) MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    B.S. Shastry, Phys. Rev. Lett. 60, 639 (1988) ADSCrossRefGoogle Scholar
  32. 32.
    B.S. Shastry, B. Sutherland, Phys. Rev. Lett. 47, 964 (1981) ADSCrossRefGoogle Scholar
  33. 33.
    W. Zheng, C.J. Hamer, R.R.P. Singh, S. Trebst, H. Monien, Phys. Rev. B. 63, 144411 (2001) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of PhysicsBose InstituteKolkataIndia

Personalised recommendations