Advertisement

Exact solutions of the Holstein model with different site energies

Solids and Liquids

Abstract.

The two-site Holstein model with different site energies, the simplest model to mimic disorder, is analytically studied by a diagonalization method of coherent states. The solutions obtained in our work are exact, and agree well with those derived by a modified Lang-Firsov (MLF) method in the weak- and strong-coupling regimes. The deviation from the MLF solution in the intermediate-coupling regime implies that our solution, including the higher order correlation terms overlooked in the MLF treatment, gives a more accurate description. To check the validity of our approach, we have also calculated the case with the same site energies, which shows that our exact solution could be consistent with a previous treatment of the Holstein model using the coherent expansion method [Phys. Rev. B 65, 174303 (2002)]. The method and the results in the present work would be useful for testing various approximate methods for the Holstein model, and are applicable to more complicated situations.

PACS.

71.38.-k Polarons and electron-phonon interactions 63.20.Kr Phonon-electron and phonon-phonon interactions 71.10.-w Theories and models of many-electron systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. Holstein, Ann. Phys. (NY) 8, 325 (1959) CrossRefADSGoogle Scholar
  2. A.B. Migdal, Sol. Phys. JETP 7, 996 (1958); S. Engelsberg, J.R. Schrieffer, Phys. Rev. 131, 993 (1963); A.S. Alexandrov, J.R. Schrieffer, Phys. Rev. B 56, 13731 (1997) Google Scholar
  3. A.S. Alexandrov, N.F. Mott, Rep. Prog. Phys. 57, 1197 (1994) CrossRefADSGoogle Scholar
  4. G. Zhao, K. Conder, H. Keller, K.A. Muler, Nature 381, 676 (1996); G. Zhao, K. Conder, H. Keller, K.A. Muler, Nature 385, 236 (1997) CrossRefADSGoogle Scholar
  5. W.P. Su, J.R. Schrieffer, A.J. Heeger, Phys. Rev. Lett. 42, 1698 (1979) CrossRefADSGoogle Scholar
  6. W.L. Warren et al., Appl. Phys. Lett. 65, 1018 (1994); K.-H. Yoo et al., Phys. Rev. Lett. 87, 198102 (2001) CrossRefADSGoogle Scholar
  7. L.G. Lang, Y.A. Firsov, Sov. Phys. JETP 16, 1301 (1963) Google Scholar
  8. J. Ranninger, Z. Phys. B: Cond. Mat. 84, 167 (1991) CrossRefGoogle Scholar
  9. I. Meccoli, M. Copone, Phys. Rev. B 63, 014303 (2001) CrossRefADSGoogle Scholar
  10. F.X. Bronold, A. Sexena, A.R. Bishop, Phys. Rev. B 63, 235109 (2001) CrossRefADSGoogle Scholar
  11. A.N. Das, P. Chaudhury, Phys. Rev. B 49, 13219 (1994) CrossRefADSGoogle Scholar
  12. J. Chatterjee, A.N. Das, Phys. Rev. B 61, 4592 (2000) CrossRefADSGoogle Scholar
  13. V.V. Kabanov, D.K. Ray, Phys. Lett. A 186, 438 (1994) CrossRefADSGoogle Scholar
  14. A.S. Alexandrov, V.V. Kabanov, D.K. Ray, Phys. Rev. B 49, 9915 (1994) CrossRefADSMathSciNetGoogle Scholar
  15. F. Marsiglio, Phys. Lett. A 180, 280 (1993); F. Marsiglio, Physica C 244, 21 (1995) CrossRefADSGoogle Scholar
  16. J. Raninger, U. Thibblin, Phys. Rev. B 45, 7730 (1992) CrossRefADSGoogle Scholar
  17. A.S. Alexandrov, Phys. Rev. B 61, 12315 (2000) CrossRefADSGoogle Scholar
  18. M. Capone, S. Ciuchi, Phys. Rev. B 65, 104409 (2002) CrossRefADSGoogle Scholar
  19. Y. Takada, A. Chatterjee, Phys. Rev. B 67, 081102 (2003) CrossRefADSGoogle Scholar
  20. R.-S. Han, Z.-J. Lin, K.L. Wang, Phys. Rev. B 65, 174303 (2002) CrossRefGoogle Scholar
  21. K.-L. Wang, Q.-H. Chen, S.-L. Wan, Phys. Lett. A 185, 216 (1994) CrossRefADSGoogle Scholar
  22. K.-L. Wang, Y. Wang, S.-L. Wan, Phys. Rev. B 54, 12852 (1996) CrossRefADSGoogle Scholar
  23. J. Chatterjee, A.N. Das, Eur. Phys. J. B 46, 481 (2005) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.The School of Science, Southwest University of Science and TechnologyMianyangP.R. China
  2. 2.The Department of Modern PhysicsUniversity of Science and Technology of ChinaHefeiP.R. China
  3. 3.State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of SciencesWuhanP.R. China

Personalised recommendations