Exact Results and Conjectures on the Adiabatic Holstein-Hubbard Model at Large Electron-Phonon Coupling

  • Serge Aubry
Part of the NATO ASI Series book series (NSSB, volume 343)


Some of the essential aspects of the propagation of electrons in solids are modelled by the simple Holstein-Hubbard model. It is a one band model that involves schematically the basic interactions between the electrons and the lattice. The Coulomb interactions of the electrons with the ions of the lattice are represented by linear on-site electron phonon couplings while the direct Coulomb electron-electron interactions are represented only by their local component as on-site Hubbard repulsions. The direct interactions between the ions of the lattice, including their Coulomb interactions, are represented phenomenologically by an elastic deformation potential.


Charge Density Wave Adiabatic Approximation Electron Phonon Coupling Small Polaron Spin Density Wave 
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. Alexandrov A.S., Ranninger J. and Robaszkiewicz S. 1986 Phys. Rev. B33 4526ADSGoogle Scholar
  2. Aubry S., Abramovici G. and Raimbault J.L. 1992 Chaotic Polaronic and Bipolaronic States in the Adiabatic Holstein Model J. Stat. Phys. 67 675–780MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. Aubry S. and Quemerais P. 1989 in Low Dimensional Electronic Properties of Molybdenum Bronzes and Oxides 295-405 Editor Claire SCHLENKER Kluwer Acad. Pub. GroupGoogle Scholar
  4. Aubry S. 1991 in Microscopic Aspects of Non-Linearity in... 105-114 ed. A.R. Bishop, V.L. Pokrovsky and V. Tognetti NATO ASI Series, Series B 264 PlenumGoogle Scholar
  5. —— 1993(a) in Phase separation in Cuprate Superconductors Edited K.A.Müller and G. Benedek World Scientific Pub. (the Science and Culture Series-Physics) 304-334Google Scholar
  6. — 1993(b) in J. Physique IV colloque C2, 3 349–355 (1993)Google Scholar
  7. —— 1994(a) The Concept of Anti-Integrability Applied to... Physica D in pressGoogle Scholar
  8. —— 1994(b) in Proceeding of Chaos, Order and Patterns: Aspects of Nonlinearity Corno Sept 1993 Ed. G. Casati Physica D to appearGoogle Scholar
  9. Aubry S. and Kuhn C. Polaronic Localisation of an Electron in a Discrete Lattice and in a Magnetic Field in preparation Baesens C. and MacKay 1994 in NonLinearity in pressGoogle Scholar
  10. Emin D. and Holstein T. 1976 Phys. Rev. Letts 36, 323ADSCrossRefGoogle Scholar
  11. Emin D. 1982 Physics Today June 1982 p.34Google Scholar
  12. Gork’ov L.P. and Lebed’ A.G. 1984 J. Physique Lett. 45 L433–L440CrossRefGoogle Scholar
  13. Kuhn C. and Aubry S. 1994 Devil’s Staircase in the Zeeman Response in the one-dimensional Half-filled adiabatic Holstein Model Submitted to J. Phys. Cond. matterGoogle Scholar
  14. Lebovitz J. and Macris N.1994 “Low Temperature Phases of...” Submitted to J. Stat. Phys. Google Scholar
  15. Raimbault J.L and Aubry S. Phase Separation in One-Dimensional Bipolaronic CDWs in preparationGoogle Scholar
  16. ]W.P. Su, J.R. Schrieffer, A.J. Heeger 1979 Phys. Rev. Lett. 42, 1968 andCrossRefGoogle Scholar
  17. J.R. Schrieffer, A.J. Heeger — 1980 Phys. Rev. B22, 2099ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Serge Aubry
    • 1
  1. 1.Laboratoire Léon Brillouin (CEA-CNRS)CE SaclayGif-sur-Yvette CédexFrance

Personalised recommendations