Quantum Monte Carlo Simulations and Weak-Coupling Approximations for the Three-Band Hubbard Model

  • R. Putz
  • H. Endres
  • A. Muramatsu
  • W. Hanke
Chapter
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NONUFM, volume 48)

Summary

We study the three-band Hubbard model for the cuprate superconductors using Quantum Monte Carlo simulations and the fluctuation exchange approximation including a self-consistent many-body renormalization of the single-particle propagator. The energy dispersion of the low-lying one-particle excitations is in very good agreement with spectroscopic measurements for a hole doping concentration δ = 0.25 of the CuO2 planes. At the same doping, we examine the spin susceptibility yielding a non-ordered phase with short-range incommensurate fluctuations near the antiferromagnetic wave vector. In the superconducting regime, the interaction vertex for the pairing correlation function in the extended s-wave channel shows a maximum for δ = 0.20, resembling the dependence of transition temperature Tc on doping.

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    For review articles on theoretical and experimental approaches to the high temperature superconductors see, for example: Proceedings of the International Conference, Kanazawa, Physica C 185–189 (1991).Google Scholar
  2. [2]
    For a review article concerning QMC techniques applied to Hubbard model see: W. von der Linden, Physics Reports, 220, 53 (1992), and references therein.Google Scholar
  3. [3]
    G. Dopf, A. Muramatsu, W. Hanke, Phys. Rev. Lett. 68, 353 (1992).CrossRefGoogle Scholar
  4. [4]
    G. Dopf, J. Wagner, P. Dieterich, A. Muramatsu, and W. Hanke, Phys. Rev. Lett. 68, 2082 (1992).CrossRefGoogle Scholar
  5. [5]
    G. Dopf, A. Muramatsu, W. Hanke, Europhys. Lett. 17, 559 (1992).CrossRefGoogle Scholar
  6. [6]
    R. T. Scalettar et al. Phys. Rev. B 44, 770 (1991).CrossRefGoogle Scholar
  7. [7]
    S. R. White et al., Phys. Rev. B 40, 506 (1989).CrossRefGoogle Scholar
  8. [8]
    E. Y. Loh et al., Phys. Rev. B 41, 9301 (1990).CrossRefGoogle Scholar
  9. [9]
    N. E. Bickers and D. J. Scalapino, Annals of Physics 193, 207 (1989).CrossRefGoogle Scholar
  10. [10]
    R. Putz, P. Dieterich, and W. Hanke, Helv. Phys. Acta 65, 433 (1992).Google Scholar
  11. [11]
    J. Luo and N. E. Bickers, Phys. Rev. B 47, 12153 (1993).CrossRefGoogle Scholar
  12. [12]
    C. M. Varma, et al., Solid State Comm. 62, 681 (1987).CrossRefGoogle Scholar
  13. [13]
    V. J. Emery, Phys. Rev. Lett. 58, 2794 (1987).CrossRefGoogle Scholar
  14. [14]
    A. K. McMahan, R. M. Martin, and S. Satpathy, Phys. Rev. B 38, 6650 (1988).CrossRefGoogle Scholar
  15. [15]
    M. S. Hybertsen, M. Schlüter, and N. E. Christensen, Phys. Rev. B 39, 9028 (1989).CrossRefGoogle Scholar
  16. [16]
    N. Nücker et al., Phys. Rev. B 37, 5158 (1988).CrossRefGoogle Scholar
  17. [17]
    P. W. Anderson, Science 235, 1196 (1987).CrossRefGoogle Scholar
  18. [18]
    J. Hubbard, Proc. Roy. Soc. A276, 238 (1963).Google Scholar
  19. [19]
    R. Blankenbecler, D. J. Scalapino, and R. L. Sugar, Phys. Rev. D 24, 2278 (1981).CrossRefGoogle Scholar
  20. [20]
    J. E. Hirsch, Phys. Rev. B 31, 4403 (1985).CrossRefGoogle Scholar
  21. [21]
    H. F. Trotter, Prog. Am. Math. Soc.10, 545 (1959).MathSciNetMATHCrossRefGoogle Scholar
  22. [22]
    M. Suzuki, Prog. Theo. Phys.56, 1454 (1976).MATHCrossRefGoogle Scholar
  23. [23]
    J. Hubbard, Phys. Rev. Lett.3, 77 (1959).CrossRefGoogle Scholar
  24. [24]
    J. E. Hirsch, Phys. Rev. B 28, 4059 (1983).CrossRefGoogle Scholar
  25. [25]
    For a comprehensive review see e.g.: Dieter W. Heermann, Computer Simulation Methods in Theoretical Physics, Springer, Berlin-Heidelberg, (1986).Google Scholar
  26. [26]
    E. Y. Loh and J. E. Gubernatis, in: Electronic Phase Transistions, ed. by W. Hanke and Y. V. Kopaev, North-HollandAAA (1992).Google Scholar
  27. [27]
    A. L. Fetter and J. D. Walecka, Quantum-Theory of Many Particle Systems, New York (1971).Google Scholar
  28. [28]
    A. Muramatsu, G. Zumbach, X. Zotos, Int. J. Mod. Phys. C 3, 185 (1992).MathSciNetMATHCrossRefGoogle Scholar
  29. [29]
    J. W. Serene and D. W. Hess, Phys. Rev. B 44, 3391 (1991).CrossRefGoogle Scholar
  30. [30]
    G. Mante et al. Z. Phys. B 80, 181 (1990).CrossRefGoogle Scholar
  31. [31]
    S. R. White et al. Phys. Rev. Lett. 63, 1523 (1989).CrossRefGoogle Scholar
  32. [32]
    H. J. Vidberg and J. W. Serene, J. Low Temp. Phys. 29, 179 (1977).CrossRefGoogle Scholar
  33. [33]
    C. de Dominicis and P. C. Martin, J. Math. Phys. 5, 14 (1964); ibid., 31 (1964).CrossRefGoogle Scholar
  34. [34]
    N. E. Bickers and S. R. White, Phys. Rev. B 43, 8044 (1991).CrossRefGoogle Scholar
  35. [35]
    J. Rossat-Mignod et al., Physica B 169, 58 (1991); Physica C 185–189, 86 (1991).CrossRefGoogle Scholar
  36. [36]
    J. M. Tranquada et al., Phys. Rev. B 46, 5561 (1992).CrossRefGoogle Scholar
  37. [37]
    T. E. Mason, G. Aeppli, and H. A. Mook, Phys. Rev. Lett. 68, 1414 (1992).CrossRefGoogle Scholar
  38. [38]
    G. Dopf, A. Muramatsu, and W. Hanke, Phys. Rev. B 41, 9264 (1990).CrossRefGoogle Scholar
  39. J. B. Torrance et al., Phys. Rev. Lett. 61, 1127 (1988), and references therein.CrossRefGoogle Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1994

Authors and Affiliations

  • R. Putz
    • 1
  • H. Endres
    • 1
  • A. Muramatsu
    • 1
  • W. Hanke
    • 1
  1. 1.Physikalisches InstitutUniversität WürzburgWürzburgGermany

Personalised recommendations