Skip to main content
SpringerLink
Log in

Exact ground state of a frustrated integer-spin modified Shastry-Sutherland model

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

Abstract

We consider a two-dimensional geometrically frustrated integer-spin Heisenberg system that admits an exact ground state. The system corresponds to a decorated square lattice with two coupling constants J 1 and J 2, and it can be understood as a generalized Shastry-Sutherland model. Main elements of the spin model are suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers s and their ground state Φ will be the product state of the local singlet ground states of the trimers. We provide exact numerical data for finite lattices as well as analytical considerations to estimate the range of the existence in dependence on the ratio of the two couplings constants J 2 and J 1 and on the spin quantum number s. Moreover, we find that the magnetization curves as a function of the applied magnetic field shows plateaus and jumps. In the classical limit s → ∞ the model exhibits phases of three- and two-dimensional ground states separated by a one-dimensional (collinear) plateau state at 1/3 of the saturation magnetization.

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. Quantum Magnetism, Lecture Notes in Physics, edited by U. Schollwöck, J. Richter, D.J.J. Farnell, R.F. Bishop (Springer, Berlin, 2004), Vol. 645

  2. Introduction to Frustrated Magnetism, edited by C. Lacroix, P. Mendels, J. Mila, Springer Series in Solid-State Sciences (Springer, Berlin, 2011), Vol. 164

  3. R. Moessner, Can. J. Phys. 79, 1283 (2001)

    Article  ADS  Google Scholar 

  4. C. Castelnovo, R. Moessner, S.L. Sondhi, Nature 451, 42 (2008)

    Article  ADS  Google Scholar 

  5. L. Balents, Nature 464, 199 (2010)

    Article  ADS  Google Scholar 

  6. D.C. Mattis, The Theory of Magnetism I (Springer, Berlin, 1991)

  7. R.O. Kuzian, S.-L. Drechsler, Phys. Rev. B 75, 024401 (2007)

    Article  ADS  Google Scholar 

  8. M. Zhitomirsky, H. Tsunetsugu, Europhys. Lett. 92, 37001 (2010)

    Article  Google Scholar 

  9. S.-L. Drechsler, S. Nishimoto, R. Kuzian, J. Málek, J. Richter, J.V.D. Brink, M. Schmitt, H. Rosner, Phys. Rev. Lett. 106, 219701 (2011)

    Article  ADS  Google Scholar 

  10. H.A. Bethe, Z. Phys. 71, 205 (1931)

    Article  ADS  MATH  Google Scholar 

  11. C.K. Majumdar, D.K. Ghosh, J. Math. Phys. 10, 1399 (1969)

    Article  ADS  MathSciNet  Google Scholar 

  12. B.S. Shastry, B. Sutherland, Physica B 108, 1069 (1981)

    Article  Google Scholar 

  13. M. Albrecht, F. Mila, Europhys. Lett. 34, 145 (1996)

    Article  ADS  Google Scholar 

  14. S. Miyahara, K. Ueda, Phys. Rev. Lett. 82, 3701 (1999)

    Article  ADS  Google Scholar 

  15. A. Läuchli, S. Wessel, M. Sigrist, Phys. Rev. B 66, 014401 (2002)

    Article  ADS  Google Scholar 

  16. C. Knetter, G.S. Uhrig, Phys. Rev. Lett. 92, 027204 (2004)

    Article  ADS  Google Scholar 

  17. R. Darradi, J. Richter, D.J.J. Farnell, Phys. Rev. B 72, 104425 (2005)

    Article  ADS  Google Scholar 

  18. A. Pimpinelli, J. Phys.: Condens. Matter 3, 445 (1991)

    Article  ADS  Google Scholar 

  19. N.B. Ivanov, J. Richter, Phys. Lett. A 232, 308 (1997)

    Article  ADS  Google Scholar 

  20. J. Richter, N.B. Ivanov, J. Schulenburg, J. Phys.: Condens. Matter 10, 3635 (1998)

    Article  ADS  Google Scholar 

  21. K. Ueda, S. Miyahara, J. Phys.: Condens. Matter 11, L175 (1999)

    Article  ADS  Google Scholar 

  22. A. Koga, K. Okunishi, N. Kawakami, Phys. Rev. B 62, 5558 (2002)

    Article  ADS  Google Scholar 

  23. A. Koga, N. Kawakami, Phys. Rev. B 65, 214415 (2002)

    Article  ADS  Google Scholar 

  24. J. Schulenburg, J. Richter, Phys. Rev. B 65, 054420 (2002)

    Article  ADS  Google Scholar 

  25. H.-J. Schmidt, J. Phys. 38, 2123 (2005)

    ADS  MATH  MathSciNet  Google Scholar 

  26. G. Müller, R.E. Shrock, Phys. Rev. 32, 5845 (1985)

    Article  Google Scholar 

  27. J. Schulenburg, A. Honecker, J. Schnack, J. Richter, H.-J. Schmidt, Phys. Rev. Lett. 88, 167207 (2002)

    Article  ADS  Google Scholar 

  28. J. Richter, O. Derzhko, J. Schulenburg, Phys. Rev. Lett. 93, 107206 (2004)

    Article  ADS  Google Scholar 

  29. M.E. Zhitomirsky, H. Tsunetsugu, Phys. Rev. B 70, R100403 (2004)

    Article  ADS  Google Scholar 

  30. O. Derzhko, J. Richter, Phys. Rev. B 70, 104415 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  31. O. Derzhko, J. Richter, Eur. Phys. J. B 52, 23 (2006)

    Article  ADS  Google Scholar 

  32. M.E. Zhitomirsky, H. Tsunetsugu, Phys. Rev. B 75, 224416 (2007)

    Article  ADS  Google Scholar 

  33. M. Gaudin, J. Phys. France 37, 1087 (1976)

    Article  MathSciNet  Google Scholar 

  34. M. Gaudin, La Fonction d’Onde de Bethe Masson (Paris, 1983)

  35. J. Richter, A. Voigt, J. Phys. A 27, 1139 (1994)

    Article  ADS  Google Scholar 

  36. M. Bortz, S. Eggert, J. Stolze, Phys. Rev. B 81, 035315 (2010)

    Article  ADS  Google Scholar 

  37. H. Kageyama, K. Yoshimura, R. Stern, N.V. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C.P. Slichter, T. Goto, Y. Ueda, Phys. Rev. Lett. 82, 3168 (1999)

    Article  ADS  Google Scholar 

  38. S. Miyahara, K. Ueda, Phys. Rev. Lett. 82, 3701 (1999)

    Article  ADS  Google Scholar 

  39. D. Poilblanc, J. Riera, C.A. Hayward, C. Berthier, M. Horvatic, Phys. Rev. B 55, R11941 (1997)

    Article  ADS  Google Scholar 

  40. Y.-Z. Zheng, M.-L. Tong, W. Xue, W.-X. Zhang, X.-M. Chen, F. Grandjean, G.J. Long, Angew. Chem. Int. Ed. 46, 6076 (2007)

    Article  Google Scholar 

  41. J. Richter, J. Schulenburg, A. Honecker, D. Schmalfuß, Phys. Rev. B 70, 174454 (2004)

    Article  ADS  Google Scholar 

  42. G. Misguich, P. Sindzingre, J. Phys.: Condens. Matter 19, 145202 (2007)

    Article  ADS  Google Scholar 

  43. B.-J. Yang, A. Paramekanti, Y.B. Kim, Phys. Rev. B 81, 134418 (2010)

    Article  ADS  Google Scholar 

  44. H.-J. Schmidt, J. Richter, J. Phys. A: Math. Theor. 43, 405205 (2010)

    Article  MathSciNet  Google Scholar 

  45. K. Kodama, M. Takigawa, M. Horvatic, C. Berthier, H. Kageyama, Y. Ueda, S. Miyahara, F. Becca, F. Mila, Science 298, 395 (2002)

    Article  ADS  Google Scholar 

  46. G. Misguich, Th. Jolicœur, S.M. Girvin, Phys. Rev. Lett. 87, 097203 (2001)

    Article  ADS  Google Scholar 

  47. A. Abendschein, S. Capponi, Phys. Rev. Lett. 101, 227201 (2008)

    Article  ADS  Google Scholar 

  48. J. Dorier, K.P. Schmidt, F. Mila, Phys. Rev. Lett. 101, 250402 (2008)

    Article  ADS  Google Scholar 

  49. J. Richter, J. Schulenburg, A. Honecker, in Quantum Magnetism, Lecture Notes in Physics, edited by U. Schollwöck, J. Richter, D.J.J. Farnell, R.F. Bishop (Springer-Verlag, Berlin, 2004), Vol. 645, p. 85

  50. H. Kawamura, S. Miyashita, J. Phys. Soc. Jpn 54, 4530 (1985)

    Article  ADS  Google Scholar 

  51. M.E. Zhitomirsky, A. Honecker, O.A. Petrenko, Phys. Rev. Lett. 85, 3269 (2000)

    Article  ADS  Google Scholar 

  52. M.E. Zhitomirsky, Phys. Rev. Lett. 88, 057204 (2002)

    Article  ADS  Google Scholar 

  53. M. Moliner, D.C. Cabra, A. Honecker, P. Pujol, F. Stauffer, Phys. Rev. B 79, 144401 (2009)

    Article  ADS  Google Scholar 

  54. C. Schröder, H.-J. Schmidt, J. Schnack, M. Luban, Phys. Rev. Lett. 94, 207203 (2005)

    Article  ADS  Google Scholar 

  55. H.-J. Schmidt, M. Luban, J. Phys. A: Math. Theor. 36, 6351 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, PF 4120, 39016, Magdeburg, Germany

    J. Richter

  2. Fachbereich Physik, Universität Osnabrück, Barbarastr. 7, 49069, Osnabrück, Germany

    H. -J. Schmidt

Authors
  1. J. Richter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. -J. Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Richter.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Richter, J., Schmidt, H.J. Exact ground state of a frustrated integer-spin modified Shastry-Sutherland model. Eur. Phys. J. B 85, 179 (2012). https://doi.org/10.1140/epjb/e2012-30152-9

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2012-30152-9

Keywords

Search

Navigation