Advertisement

The European Physical Journal B

, Volume 75, Issue 2, pp 253–266 | Cite as

The embedding method beyond the single-channel case

Two-mode and Hubbard chains
  • A. Freyn
  • G. Vasseur
  • P. Schmitteckert
  • D. WeinmannEmail author
  • G.-L. Ingold
  • R. A. Jalabert
  • J.-L. Pichard
Mesoscopic and Nanoscale Systems

Abstract

We investigate the relationship between persistent currents in multi-channel rings containing an embedded scatterer and the conductance through the same scatterer attached to leads. The case of two uncoupled channels corresponds to a Hubbard chain, for which the one-dimensional embedding method is readily generalized. Various tests are carried out to validate this new procedure, and the conductance of short one-dimensional Hubbard chains attached to perfect leads is computed for different system sizes and interaction strengths. In the case of two coupled channels the conductance can be obtained from a statistical analysis of the persistent current or by reducing the multi-channel scattering problem to several single-channel setups.

Keywords

Transfer Matrix Persistent Current Transmission Amplitude Embedding Method Numerical Renormalization Group 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav, M.A. Kastner, Nature 391, 156 (1998)CrossRefADSGoogle Scholar
  2. 2.
    M. Pustilnik, L.I. Glazman, D.H. Cobden, L.P. Kouwenhoven, Lect. Notes Phys. 579, 3 (2001)CrossRefADSGoogle Scholar
  3. 3.
    A.C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1997)Google Scholar
  4. 4.
    P. Mehta, N. Andrei, Phys. Rev. Lett. 96, 216802 (2006); Erratum:P. Mehta, S.-P. Chao, N. Andrei, e-print arXiv:cond-mat/0703426v1CrossRefADSGoogle Scholar
  5. 5.
    B. Doyon, Phys. Rev. Lett. 99, 076806 (2007)CrossRefADSGoogle Scholar
  6. 6.
    E. Boulat, H. Saleur, P. Schmitteckert, Phys. Rev. Lett. 101, 140601 (2008)CrossRefMathSciNetADSGoogle Scholar
  7. 7.
    P. Schmitteckert, F. Evers, Phys. Rev. Lett. 100, 086401 (2008)CrossRefADSGoogle Scholar
  8. 8.
    Y. Meir, N.S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992)CrossRefADSGoogle Scholar
  9. 9.
    J. Favand, F. Mila, Eur. Phys. J. B 2, 293 (1998)CrossRefADSGoogle Scholar
  10. 10.
    O.P. Sushkov, Phys. Rev. B 64, 155319 (2001)CrossRefADSGoogle Scholar
  11. 11.
    R.A. Molina, D. Weinmann, R.A. Jalabert, G.-L. Ingold, J.-L. Pichard, Phys. Rev. B 67, 235306 (2003)CrossRefADSGoogle Scholar
  12. 12.
    V. Meden, U. Schollwöck, Phys. Rev. B 67, 193303 (2003)CrossRefADSGoogle Scholar
  13. 13.
    T. Rejec, A. Ramšak, Phys. Rev. B 68, 035342 (2003)CrossRefADSGoogle Scholar
  14. 14.
    R.A. Molina, P. Schmitteckert, D. Weinmann, R.A. Jalabert, G.-L. Ingold, J.-L. Pichard, Eur. Phys. J. B 39, 107 (2004)CrossRefADSGoogle Scholar
  15. 15.
    R.A. Molina, D. Weinmann, J.-L. Pichard, Eur. Phys. J. B 48, 243 (2005)CrossRefADSGoogle Scholar
  16. 16.
    The embedding method including a well-defined extrapolation procedure which is the subject of this paper should not be confused with the so-called “embedded-cluster approximation” that is based on the exact diagonalization of a finite region later connected to leads. For a recent update in that body of work see F. Heidrich-Meisner, G.B. Martins, C.A. Büsser, K.A. Al-Hassanieh, A.E. Feiguin, G. Chiappe, E.V. Anda, E. Dagotto, Eur. Phys. J. B 67, 527 (2009)CrossRefADSGoogle Scholar
  17. 17.
    A.O. Gogolin, N.V. Prokof’ev, Phys. Rev. B 50, 4921 (1994)CrossRefADSGoogle Scholar
  18. 18.
    D. Weinmann, R.A. Jalabert, A. Freyn, G.-L. Ingold, J.-L. Pichard, Eur. Phys. J. B 66, 239 (2008)CrossRefADSGoogle Scholar
  19. 19.
    G. Vasseur, Ph.D. thesis, Université Louis Pasteur Strasbourg, 2006, e-print http://eprints-scd-ulp.u-strasbg.fr:8080/574/
  20. 20.
    T. Rejec, A. Ramšak, Phys. Rev. B 68, 033306 (2003)CrossRefADSGoogle Scholar
  21. 21.
    J. Mravlje, A. Ramšak, T. Rejec, Phys. Rev. B 72, R121403 (2005)CrossRefADSGoogle Scholar
  22. 22.
    R. Žitko, J. Bonča, A. Ramšak, T. Rejec, Phys. Rev. B 73, 153307 (2006)CrossRefADSGoogle Scholar
  23. 23.
    P.A. Mello, J.-L. Pichard, J. Phys. I 1, 493 (1991)CrossRefGoogle Scholar
  24. 24.
    C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997)CrossRefADSGoogle Scholar
  25. 25.
    R.A. Jalabert, J.-L. Pichard, J. Phys. I 5, 287 (1995)CrossRefGoogle Scholar
  26. 26.
    X. Waintal, G. Fleury, K. Kazymyrenko, M. Houzet, P. Schmitteckert, D. Weinmann, Phys. Rev. Lett. 101, 106804 (2008)CrossRefADSGoogle Scholar
  27. 27.
    S.R. White, Phys. Rev. Lett. 69, 2863 (1992)CrossRefADSGoogle Scholar
  28. 28.
    Density-Matrix Renormalization — A New Numerical Method in Physics edited by I. Peschel, X. Wang, M. Kaulke, K. Hallberg, Lect. Notes Phys. 528, 1 (Springer, Berlin, 1999)Google Scholar
  29. 29.
    P. Schmitteckert, Ph. D. thesis, Universität Augsburg, 1996Google Scholar
  30. 30.
    A. Oguri, Phys. Rev. B 63, 115305 (2001)CrossRefADSGoogle Scholar
  31. 31.
    Y. Nisikawa, A. Oguri, Phys. Rev. B 73, 125108 (2006)CrossRefADSGoogle Scholar
  32. 32.
    A. Oguri, Phys. Rev. B 59, 12240 (1999)CrossRefADSGoogle Scholar
  33. 33.
    A. Oguri, A.C. Hewson, J. Phys. Soc. Jpn 74, 988 (2005)zbMATHCrossRefADSGoogle Scholar
  34. 34.
    P. Schmitteckert, R. Werner, Phys. Rev. B 69, 195115 (2004)CrossRefADSGoogle Scholar
  35. 35.
    M. Vekić, S.R. White, Phys. Rev. Lett. 71, 4283 (1993)zbMATHCrossRefMathSciNetADSGoogle Scholar
  36. 36.
    D. Bohr, P. Schmitteckert, P. Wölfle, Europhys. Lett. 73, 246 (2006)CrossRefADSGoogle Scholar
  37. 37.
    D. Bohr, P. Schmitteckert, Phys. Rev. B 75, R241103 (2007)CrossRefADSGoogle Scholar
  38. 38.
    E.V. Anda, G. Chiappe, C.A. Büsser, M.A. Davidovich, G.B. Martins, F. Heidrich-Meisner, E. Dagotto, Phys. Rev. B 78, 085308 (2008)CrossRefADSGoogle Scholar
  39. 39.
    T.K. Ng, P.A. Lee, Phys. Rev. Lett. 61, 1768 (1988)CrossRefADSGoogle Scholar
  40. 40.
    A. Freyn, J.-L. Pichard, Phys. Rev. B 81, 085108 (2010)CrossRefADSGoogle Scholar

Copyright information

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

Authors and Affiliations

  • A. Freyn
    • 1
    • 2
  • G. Vasseur
    • 3
  • P. Schmitteckert
    • 4
  • D. Weinmann
    • 3
    Email author
  • G.-L. Ingold
    • 5
  • R. A. Jalabert
    • 3
  • J.-L. Pichard
    • 1
  1. 1.Service de Physique de l’État Condensé (CNRS URA 2464), IRAMIS/SPEC, CEA SaclayGif-sur-Yvette CedexFrance
  2. 2.Institut NéelGrenoble Cedex 9France
  3. 3.Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 (UdS-CNRS)Strasbourg Cedex 2France
  4. 4.Institut für Nanotechnologie, Karlsruher Institut für TechnologieEggenstein-LeopoldshafenGermany
  5. 5.Institut für Physik, Universität AugsburgAugsburgGermany

Personalised recommendations