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Drude Weight and f-Sum Rule of the Hubbard Model at Strong Coupling

  • Peter Horsch
  • Walter Stephan
Chapter
  • 390 Downloads
Part of the NATO ASI Series book series (NSSB, volume 343)

Abstract

The motion of holes in the two-dimensional single-band Hubbard and t-J model is intimately related to the dynamics of holes or electrons doped in copper-oxide based superconductors.1,2 The latter model is supposed to describe the low-energy physics in a partially filled Hubbard band. Transitions accross the Hubbard gap are integrated out and give rise to the effective antiferromagnetic Heisenberg interaction among the (Cu)-spins in the t-J Hamiltonian. The optical conductivity3–5 and the Drude weight6–10 of the 2D Hubbard and t-J models have been studied recently by several authors using Lanczos diagonalization techniques. There exist also studies for two-band models which include explicitely Cu and 0 orbitals in the unit cell.11 Characteristic for the Hubbard model is a fast decrease of absorption into the upper Hubbard band upon doping.5 The spectral weight is transfered to the lower Hubbard band, and gives rise to a Drude peak at zero energy (in the absence of impurities) and in the 2D case to a rapid growth of a broad absorption band at finite frequency. This has led several authors to suggest that the anomalous midinfrared absorption observed in all doped copper oxides12,13 may have a natural explanation in this framework in the broad absorption band resulting from the strong coupling of the charge carriers to the spin degrees of freedom4,5. The Bethe Ansatz soluble one-dimensional models appear to be different due to spin-charge decoupling. As a consequence the dissipative part of their spectra is very small3,5,9 and almost all spectral weight is in the Drude peak14–18.

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References

  1. 1.
    P.W. Anderson, Science 235, 1196 (1987).ADSCrossRefGoogle Scholar
  2. 2.
    F. C. Zhang and T. M. Rice, Phys. Rev. B 37, 3759 (1988).ADSCrossRefGoogle Scholar
  3. 3.
    I. Sega and P. Prelovsek, Phys. Rev. B 42, 892 (1990).ADSCrossRefGoogle Scholar
  4. 4.
    A. Moreo and E. Dagotto, Phys. Rev. B 42, 4786 (1990).ADSCrossRefGoogle Scholar
  5. 5.
    W. Stephan and P. Horsch, Phys. Rev. B 42, 8736 (1990).ADSCrossRefGoogle Scholar
  6. 6.
    X. Zotos, P. Prelovsek, and I. Sega, Phys. Rev. B 42, 8445 (1990).ADSCrossRefGoogle Scholar
  7. 7.
    D. Poilblanc and E. Dagotto, Phys. Rev. B 44, 466 (1991).ADSCrossRefGoogle Scholar
  8. 8.
    D. Poilblanc, Phys. Rev. B 44, 9562 (1991).ADSCrossRefGoogle Scholar
  9. 9.
    R.M. Fye, M.J. Martins, D.J. Scalapino, J. Wagner, and W. Hanke, Phys. Rev. B 44, 6909 (1991).ADSCrossRefGoogle Scholar
  10. 10.
    W. Stephan and P. Horsch, Int. J. Mod. Phys. B 6, 589 (1992).ADSCrossRefGoogle Scholar
  11. 11.
    E. Y. Loh, T. Martin, P. Prelovsek, and D. K. Campbell, Phys. Rev. B 38, 2494 (1988).ADSCrossRefGoogle Scholar
  12. 12.
    T. Timusk et al., Physica C 162–164, 841 (1989).CrossRefGoogle Scholar
  13. 13.
    S. Uchida, Mod. Phys. Lett. B 4, 513 (1991) and references therein.ADSCrossRefGoogle Scholar
  14. 14.
    H.J. Schulz, Phys. Rev. Lett. 64, 2831 (1990).ADSCrossRefGoogle Scholar
  15. 15.
    B.S. Shastry and B. Sutherland, Phys. Rev. Lett. 65, 243 (1990).MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. 16.
    N. Kawakami and S.-K. Yang, Phys. Rev. Lett. 65, 3063 (1990); and Phys. Rev. B 44, 7844 (1991).MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    C.A. Stafford, A.J. Millis, and B.S. Shastry, Phys. Rev. B 43, 13660 (1991).ADSCrossRefGoogle Scholar
  18. 18.
    J.M.P. Carmelo and P. Horsch, Phys. Rev. Lett. 68 871 (1992).ADSCrossRefGoogle Scholar
  19. 19.
    C. L. Kane, P. A. Lee and N. Read, Phys. Rev. B 39, 6880 (1989).ADSCrossRefGoogle Scholar
  20. 20.
    P. Horsch, W. Stephan, K. V. Szczepanski, M. Ziegler, and W. V. D. Linden, Physica C 162–164 783 (1989).CrossRefGoogle Scholar
  21. 21.
    E. Dagotto et al, Phys. Rev. B 41, 811 (1990).ADSCrossRefGoogle Scholar
  22. 22.
    K. J. von Szczepanski et al, ibid., 2017 (1990).Google Scholar
  23. 23.
    F. Marsiglio et al, Phys. Rev. B 43, 10882 (1991).ADSCrossRefGoogle Scholar
  24. 24.
    G. Martinez and P. Horsch, Phys. Rev. B 44, 317 (1991).ADSCrossRefGoogle Scholar
  25. 25.
    W. Stephan and P. Horsch, Phys. Rev. Lett. 66, 2258 (1991).ADSCrossRefGoogle Scholar
  26. 26.
    E. Dagotto, F. Ortolani, and D. Scalapino, Phys. Rev. B 46, 3183 (1992).ADSCrossRefGoogle Scholar
  27. 27.
    G. Dopf, J. Wagner, P. Dieterich, A. Muramatsu, and W. Hanke, Phys. Rev. Lett. 68, 2082 (1992).ADSCrossRefGoogle Scholar
  28. 28.
    W. Kohn, Phys. Rev. 133, A171 (1964).MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    We assume here the special case only to keep notations simple. In our implementation of the algorithm \( \vec A = \left( {{A_\alpha },{A_\beta }} \right) \) can point in an arbitrary direction.Google Scholar
  30. 30.
    D. Baeriswyl, J. Carmelo, and A. Luther, Phys. Rev. B 16, 7247 (1986).ADSCrossRefGoogle Scholar
  31. 31.
    P. Horsch and W. Stephan, Phys. Rev. B 48 10595 (1993).ADSCrossRefGoogle Scholar
  32. 32.
    H. E. Castillo and C. A. Balseiro, Phys. Rev. Lett. 68 121 (1992).ADSCrossRefGoogle Scholar
  33. 33.
    A.G. Rojo, G. Kotliar, and G. Canright, Phys. Rev. B 47 9140 (1993).ADSCrossRefGoogle Scholar
  34. 34.
    N. Furukawa and M. Imada, J. Phys. Soc. Jpn. 62 2557 (1993).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Peter Horsch
    • 1
  • Walter Stephan
    • 2
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgartFed. Rep. Germany
  2. 2.King’s College LondonStrand, LondonUK

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