The Hubbard Model for One-Dimensional Solids

  • Anna Painelli
  • Alberto Girlando
Part of the NATO ASI Series book series (NSSB, volume 213)


In recent years several unambiguous experimental evidences have been found stressing the relevance of electron-electron (e-e) interaction in one-dimensional (1D) solids, either charge-transfer salts1 or polymers.2 However there is not agreement between physicists on how to model e-e interaction in polymers, so that the effects of such interaction on the dimerization amplitude and on the band gap are still controversial.3–13 The Hubbard model14 has been generally adopted to investigate the role of e-e interaction in 1D solids. It is the solid state counterpart of the Pariser-Parr-Pople (PPP) model, widely tested and successfully applied in molecular physics. However, the electrons in isolated molecules experience an unscreened Coulomb repulsion, whereas in 1D solids the interaction between the electrons along a chain may be screened due to the presence of mobile electrons on neighboring chains. The applicability of Hubbard model to systems with highly screened potential still has to be settled.


Hubbard Model Short Range Potential Neighboring Chain Effective Attraction Short Range Repulsion 
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.
    S. Mazumdar and S.N. Dixit, Phys.Rev.B 34:3683 (1986) and references therein.CrossRefADSGoogle Scholar
  2. 2.
    Z.G. Soos and G.W. Hayden, in: “Electroresponsive Polymeric Systems”, T. Skotheim ed., M. Dekker, New York (1988), p.197 and references therein.Google Scholar
  3. 3.
    S. Kivelson, W.-P. Su, J.R. Schrieffer, and A. Heeger, Phys.Rev.Lett. 58: 1899 (1987).CrossRefADSGoogle Scholar
  4. 4.
    C. Wu, X. Sun, and K. Nasu, Phys.Rev.Lett. 59: 72 (1988).Google Scholar
  5. 5.
    D. Baeriswyl, P. Horsch, and K. Maki, Phys.Rev.Lett. 60: 70 (1988).CrossRefADSGoogle Scholar
  6. 6.
    J.T.Gammel and D.K.Campbell, Phys.Rev.Lett. 60: 72 (1988).CrossRefADSGoogle Scholar
  7. 7.
    S. Kivelson, W.-P. Su, J.R. Schrieffer, A. Heeger, Phys.Rev.Lett. 60: 73 (1988).CrossRefADSGoogle Scholar
  8. 8.
    A. Painelli and A. Girlando, Solid State Commun. 66: 273 (1988).CrossRefADSGoogle Scholar
  9. 9.
    Z.G. Soos and G.W. Hayden, Mol.Cryst.Liq.Cryst. 160: 421 (1988).Google Scholar
  10. 10.
    A. Painelli and A. Girlando, Synth. Metals 27:15 (1988) and Phys. Rev. B, in press.CrossRefGoogle Scholar
  11. 11.
    D.K. Campbell, J.T. Gammel, and E.Y. Loh, Phys.Rev.B, in press.Google Scholar
  12. 12.
    J. Voit, Diagonal and Off-Diagonal Electronic Interactions and Phonon Dynamics in an Extended Model of Polyacetylerie, this book; J. Voit, Synth.Metals, in press.Google Scholar
  13. 13.
    V. Waas, J. Voit, and H. Büttner, Synth.Metals, in press.Google Scholar
  14. 14.
    P.W. Anderson, Phys.Rev. 115:2 (1959); J.Hubbard, Proc.R.Soc.London A276:238 (1963) and Phys.Rev.B 17: 494 (1978).CrossRefMATHADSMathSciNetGoogle Scholar
  15. 15.
    L. Salem, “The Molecular Orbital Theory of Conjugated Systems”, Benjamin, New York (1966).Google Scholar
  16. 16.
    N.W. Ashcroft and N.D. Mermin, “Solid State Physics”, Holt Saunders, London (1976), chap. 10.Google Scholar
  17. 17.
    R.S. Mulliken, J.Chim.Phys. (Paris) 46: 675 (1949).Google Scholar
  18. 18.
    Since for large intersite distances multi-center integrals are strongly dominated by the exponential decay of the site orbitals, we believe that the results obtained with the carbon 2pπ Slater orbitals are applicable, at least for small S, to any choice of atomic or molecular site orbitals.Google Scholar
  19. 19.
    R.S. Mulliken et al., J.Chem.Phys. 17: 1248 (1949).CrossRefADSGoogle Scholar
  20. 20.
    J. Hirschfelder, H. Eyring, and N. Rosen, J.Chem.Phys. 4: 121 (1936).CrossRefADSGoogle Scholar
  21. 21.
    The large absolute values of X, W, Y and X’ terms in the S≳ 0.75 regime are due to the vanishing of U in this regime, where the S expansion is clearly unphysical. Moreover in evaluating X’ we have always retained the S’ terms, even if they should be neglected for S≳ 0.25. The results are not qualitatively modified.Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • Anna Painelli
    • 1
  • Alberto Girlando
    • 2
  1. 1.Dept. of Chemical PhysicsPadova UniversityPadovaItaly
  2. 2.Inst. of Chemical PhysicsParma UniversityParmaItaly

Personalised recommendations