Skip to main content
SpringerLink
Log in

Delocalization of two interacting particles in the 2D Harper model

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

Abstract

We study the problem of two interacting particles in a two-dimensional quasiperiodic potential of the Harper model. We consider an amplitude of the quasiperiodic potential such that in absence of interactions all eigenstates are exponentially localized while the two interacting particles are delocalized showing anomalous subdiffusive spreading over the lattice with the spreading exponent b ≈ 0.5 instead of a usual diffusion with b = 1. This spreading is stronger than in the case of a correlated disorder potential with a one particle localization length as for the quasiperiodic potential. At the same time we do not find signatures of ballistic pairs existing for two interacting particles in the localized phase of the one-dimensional Harper model.

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. P.G. Harper, Proc. Phys. Soc. London A 68, 874 (1955)

    Article  ADS  Google Scholar 

  2. D.R. Hofstadter, Phys. Rev. B 14, 2239 (1976)

    Article  ADS  Google Scholar 

  3. S. Aubry, G. André, Ann. Israel Phys. Soc. 3, 133 (1980)

    Google Scholar 

  4. J.B. Sokoloff, Phys. Rep. 126, 189 (1985)

    Article  ADS  Google Scholar 

  5. S.Y. Jitomirskaya, Ann. Math. 150, 1159 (1999)

    Article  MathSciNet  Google Scholar 

  6. D.L. Shepelyansky, Phys. Rev. B 54, 14896 (1996)

    Article  ADS  Google Scholar 

  7. A. Barelli, J. Bellissard, Ph. Jacquod, D.L. Shepelyansky, Phys. Rev. Lett. 77, 4752 (1996)

    Article  ADS  Google Scholar 

  8. G. Dufour, G. Orso, Phys. Rev. Lett. 109, 155306 (2012)

    Article  ADS  Google Scholar 

  9. D.L. Shepelyansky, Phys. Rev. Lett. 73, 2607 (1994)

    Article  ADS  Google Scholar 

  10. Y. Imry, Europhys. Lett. 30, 405 (1995)

    Article  ADS  Google Scholar 

  11. D. Weinmann, A. Müller-Groeling, J.-L. Pichard, K. Frahm, Phys. Rev. Lett. 75, 1598 (1995)

    Article  ADS  Google Scholar 

  12. K. Frahm, A. Müller-Groeling, J.-L. Pichard, D. Weinmann, Europhys. Lett. 31, 169 (1995)

    Article  ADS  Google Scholar 

  13. F. von Oppen, T. Wetting, J. Müller, Phys. Rev. Lett. 76, 491 (1996)

    Article  ADS  Google Scholar 

  14. F. Borgonovi, D.L. Shepelyansky, J. Phys. I France 6, 287 (1996)

    Article  Google Scholar 

  15. D.L. Shepelyansky, in Correlated fermions and transport in mesoscopic systems, edited by T. Martin, G. Montambaux, J. Tran Thanh Van (Editions Frontieres, Gif-sur-Yvette, 1996), p. 201

  16. K.M. Frahm, Eur. Phys. J. B 10, 371 (1999)

    Article  ADS  Google Scholar 

  17. D.L. Shepelyansky, Phys. Rev. B 61, 4588 (2000)

    Article  ADS  Google Scholar 

  18. J. Lages, D.L. Shepelyansky, Eur. Phys. J. B 21, 129 (2001)

    Article  ADS  Google Scholar 

  19. S. Flach, M. Ivanchenko, R. Khomeriki, Europhys. Lett. 98, 66002 (2012)

    Article  ADS  Google Scholar 

  20. K.M. Frahm, D.L. Shepelyansky, Eur. Phys. J. B 88, 337 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  21. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature 453, 895 (2008)

    Article  ADS  Google Scholar 

  22. E. Lucioni, B. Deissler, L. Tanzi, G. Roati, M. Zaccanti, M. Modugno, M. Larcher, F. Dalfovo, M. Inguscio, G. Modugno, Phys. Rev. Lett. 106, 230403 (2011)

    Article  ADS  Google Scholar 

  23. M. Schreiber, S.S. Hodgman, P. Bordia, H. Lüschen, M.H. Fischer, R. Vosk, E. Altman, U. Schneider, I. Bloch, Science 349, 842 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  24. P. Bordia, H.K. Lüschen, S.S. Hodgman, M. Schreiber, I. Bloch, U. Schneider, arXiv:1509.00478 (2015)

  25. A.S. Pikovsky, D.L. Shepelyansky, Phys. Rev. Lett. 100, 094101 (2008)

    Article  ADS  Google Scholar 

  26. I. Garcia-Mata, D.L. Shepelyansky, Phys. Rev. E 79, 026205 (2009)

    Article  ADS  Google Scholar 

  27. M. Frigo, in Proceeding of 1999 ACM SIGPLAN Conf. “Programming Language Design and Implementation (PLDI ‘99)”, Atlanta, Georgia, 1999, http://www.fftw.org/pldi99.pdf

  28. J. Lages, D.L. Shepelyansky, Phys. Rev. B 64, 094502 (2001)

    Article  ADS  Google Scholar 

  29. T.V. Lapteva, M.V. Ivanchenko, S. Flach, J. Phys. A 47, 493001 (2014)

    Article  Google Scholar 

  30. J. Bourgain, S. Jitomirskaya, Invent. Math. 148, 453 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  31. S. Jitomirskaya, C.A. Marx, arXiv:1503.05740 (2015)

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062, Toulouse, France

    Klaus M. Frahm & Dima L. Shepelyansky

Authors
  1. Klaus M. Frahm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dima L. Shepelyansky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dima L. Shepelyansky.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Frahm, K., Shepelyansky, D. Delocalization of two interacting particles in the 2D Harper model. Eur. Phys. J. B 89, 8 (2016). https://doi.org/10.1140/epjb/e2015-60787-7

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2015-60787-7

Keywords

Search

Navigation