Skip to main content

Varied perturbation theory for the dispersion dip in the two-dimensional Heisenberg quantum antiferromagnet

Abstract

We study the roton-like dip in the magnon dispersion at the boundary of the Brillouin zone in the isotropic S = 1/2 Heisenberg quantum antiferromagnet. This high-energy feature is sometimes seen as indication of a fractionalization of the magnons to spinons. In this article, we provide evidence that the description of the dip in terms of magnons can be improved significantly by applying more advanced evaluation schemes. In particular, we illustrate the usefulness of the application of the principle of minimal sensitivity in varied perturbation theory. Thereby, we provide an example for the application of this approach to an extended condensed matter problem governed by correlations which can trigger analogous investigations for many other systems.

This is a preview of subscription content, access via your institution.

References

  1. E. Manousakis, Rev. Mod. Phys. 63, 1 (1991)

    ADS  Article  Google Scholar 

  2. K. Majumdar, D. Furton, G.S. Uhrig, Phys. Rev. B 85, 144420 (2012)

    ADS  Article  Google Scholar 

  3. M. Le Tacon, G. Ghiringhelli, J. Chaloupka, M.M. Sala, V. Hinkov, M. Haverkort, M. Minola, M. Bakr, K.J. Zhou, S. Blanco-Canosa, C. Monney, Y.T. Song, G.L. Sun, C.T. Lin, G.M.D. Luca, M. Salluzzo, G. Khaliullin, T. Schmitt, L. Braicovic, B. Keimer, Nat. Phys. 7, 725 (2011)

    Article  Google Scholar 

  4. R.R.P. Singh, M.P. Gelfand, Phys. Rev. B 52, 15695 (1995)

    ADS  Article  Google Scholar 

  5. W. Zheng, J. Oitmaa, C.J. Hamer, Phys. Rev. B 71, 184440 (2005)

    ADS  Article  Google Scholar 

  6. A.W. Sandvik, R.R.P. Singh, Phys. Rev. Lett. 86, 528 (2001)

    ADS  Article  Google Scholar 

  7. J. Igarashi, Phys. Rev. Lett. 46, 10763 (1992)

    Google Scholar 

  8. C.J. Hamer, W. Zheng, P. Arndt, Phys. Rev. B 46, 6276 (1992)

    ADS  Article  Google Scholar 

  9. J. Igarashi, T. Nagao, Phys. Rev. B 72, 014403 (2005)

    ADS  Article  Google Scholar 

  10. A.V. Syromyatnikov, J. Phys. C 22, 216003 (2010)

    Google Scholar 

  11. H.M. Rønnow, D.F. McMorrow, R. Coldea, A. Harrison, I.D. Youngson, T.G. Perring, G. Aeppli, O. Syljuåsen, K. Lefmann, C. Rischel, Phys. Rev. Lett. 87, 037202 (2001)

    ADS  Article  Google Scholar 

  12. N.B. Christensen, D.F. McMorrow, H.M. Rønnow, A. Harrison, T.G. Perring, R. Coldea, J. Magn. Magn. Mater. 272-276, 896 (2004)

    ADS  Article  Google Scholar 

  13. N.B. Christensen, H.M. Rønnow, D.F. McMorrow, A. Harrison, T.G. Perring, M. Enderle, R. Coldea, L.P. Regnault, G. Aeppli, Proc. Natl. Acad. Sci. 104, 15264 (2007)

    ADS  Article  Google Scholar 

  14. N.S. Headings, S.M. Hayden, R. Coldea, T.G. Perring, Phys. Rev. Lett. 105, 247001 (2010)

    ADS  Article  Google Scholar 

  15. C. Knetter, K.P. Schmidt, M. Grüninger, G.S. Uhrig, Phys. Rev. Lett. 87, 167204 (2001)

    ADS  Article  Google Scholar 

  16. K.P. Schmidt, G.S. Uhrig, Mod. Phys. Lett. B 19, 1179 (2005)

    ADS  Article  Google Scholar 

  17. C. Knetter, G.S. Uhrig, Eur. Phys. J. B 13, 209 (2000)

    ADS  Article  Google Scholar 

  18. S. Trebst, H. Monien, C.J. Hamer, Z. Weihong, R.R.P. Singh, Phys. Rev. Lett. 85, 4373 (2000)

    ADS  Article  Google Scholar 

  19. P.M. Stevenson, Phys. Rev. D 23, 2916 (1981)

    ADS  Article  Google Scholar 

  20. S. Dusuel, G.S. Uhrig, J. Phys. A 37, 9275 (2004)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  21. F.J. Dyson, Phys. Rev. 102, 1217 (1956)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  22. F.J. Dyson, Phys. Rev. 102, 1230 (1956)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  23. S.V. Maleev, Zh. Eksp. Teor. Fiz. 33, 1010 (1957)

    Google Scholar 

  24. S.V. Maleev, Sov. Phys. JETP 6, 776 (1958)

    ADS  Google Scholar 

  25. A.W. Sandvik, Phys. Rev. B 56, 11678 (1997)

    ADS  Article  Google Scholar 

  26. H. Krull, N.A. Drescher, G.S. Uhrig, Phys. Rev. B 86, 125113 (2012)

    ADS  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Götz S. Uhrig.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Uhrig, G., Majumdar, K. Varied perturbation theory for the dispersion dip in the two-dimensional Heisenberg quantum antiferromagnet. Eur. Phys. J. B 86, 282 (2013). https://doi.org/10.1140/epjb/e2013-40159-3

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2013-40159-3

Keywords

  • Solid State and Materials