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Spin Dynamics of Cuprate Superconductors: Exact Results from Numerical Continued Fraction Expansions

  • C.-X. Chen
  • H.-B. Schüttler
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 45)

Abstract

We present the first results for the T = 0 dynamical structure factor of finite-sized 2D square-lattice spin-1/2 antiferromagnetic Heisenberg systems with up to 16 spins, obtained by numerical continued fraction expansion techniques. Our results are compared to a recently proposed Schwinger boson mean-field theory. We find that the mean-field theory represents an excellent approximation to the exact spin excitation spectra and to the static structure factor. for all system sizes studied. We also show the results for the spin dynamics in the presence of a dopant induced hole carrier, describe by either single or multi-orbital Hubbard models

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References

  1. (1).
    For a review see: R. J. Birgeneau and G. Shirane, in “Physical Properties of High Temperature Superconductors”, D.M. Ginsberg Ed., World Scientific Publishing, Feb. 1989 (in press).Google Scholar
  2. (2).
    E. Manousakis and R. Salvador, Phys. Rev. Lett. 60, 840(1988); Phys. Rev. B 38 (1988) (in press).CrossRefADSGoogle Scholar
  3. (3)(a).
    J. D. Reger and A. P. Young, Phys Rev B 37, 5978 (1988).CrossRefADSGoogle Scholar
  4. (3)(b).
    J. D. Reger, J. A. Riera, and A. P. Young, preprint.Google Scholar
  5. (4).
    S. Tang and H. Lin, Phys. Rev. B 38 ), 6863 (1988).CrossRefADSGoogle Scholar
  6. (5).
    T. Barnes and E. S. Swanson, Phys. Rev. B 37, 9405 (1988).CrossRefADSGoogle Scholar
  7. (6).
    E. Dagotto and A. Moreo, Phys. Rev. B 38, 5087 (1988).CrossRefADSGoogle Scholar
  8. (7).
    J. E. Hirsch and S. Tang, UCSD preprint (1988) (to be published); S. Tang and J. E. Hirsch, UCSD preprint (1988) (to be published).Google Scholar
  9. (8).
    S. Chakravarty, B. I. Halperin and D. R. Nelson, Phys Rev. Lett. 60, 1057 (1988).CrossRefADSGoogle Scholar
  10. (9).
    D. A. Huse Phys. Rev. B 37, 2380 (1988); D.A. Huse and V. Elser, Phys. Rev. Lett. 60, 2531 (1988).CrossRefADSGoogle Scholar
  11. (10).
    S. Miyashita, J. Phys. Soc. Jap. 57, 1934 (1988).CrossRefGoogle Scholar
  12. (11).
    J. Oitmaa and D. D. Betts, Can. J. Phys. 56, 897 (1978).CrossRefADSGoogle Scholar
  13. (12).
    P. W. Anderson, Science 235, 1196 (1987); G. Baskaran, Z. Zou, and P.W. Anderson, Solid State Commun. 63, 973 (1987).CrossRefADSGoogle Scholar
  14. (13).
    I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988).CrossRefADSGoogle Scholar
  15. (14)(a).
    D. Arovas and A. Auerbach, Phys. Rev. B 38, 316 (1988);CrossRefADSGoogle Scholar
  16. (14)(b).
    A. Auerbach and D. P. Arovas, Phys. Rev. Lett. 61 617 (1988).CrossRefADSMathSciNetGoogle Scholar
  17. (15).
    M. Takahashi, Phys. Rev. Lett. 58, 168 (1987); Phys. Rev. B 36, 3791 (1986); University of Tokyo, ISSP, preprint Ser. A No. 2091 (1989) (to be published).CrossRefADSGoogle Scholar
  18. (16).
    H. Mori, Prog. Theor. Phys. 34, 399 (1965); ibid. 33, 423 (1965).CrossRefADSGoogle Scholar
  19. (17).
    M. H. Lee, Phys. Rev. Lett. 49, 1072 (1982); Phys. Rev. B 26, 1072 (1982); J. Math. Phys. 24, 2512 (1983).CrossRefADSGoogle Scholar
  20. (18).
    E. R. Gagliano and C. A. Balseiro, Phys. Rev. Lett. 59, 2999 (1987); Phys. Rev. B 38, 11766 (1988).CrossRefADSGoogle Scholar
  21. (19).
    E. Y. Loh and D. Campbell, Synth. Metals bf 27, 499 (1988)CrossRefGoogle Scholar
  22. (20).
    E. R. Gagliano, E. Dagotto, A. Moreo, and F. C. Alcaraz, Phys. Rev. B 34, 1677 (1986).CrossRefADSGoogle Scholar
  23. (21).
    N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17 1133 (1966).CrossRefADSGoogle Scholar
  24. (22).
    T. Oguchi, Phys. Rev. 117, 117 (1960).CrossRefMATHADSGoogle Scholar
  25. (23).
    N. E. Bickers, Rev. Mod. Phys. 59, 845 (1987).CrossRefADSGoogle Scholar
  26. (24).
    Statical correlation functions and susceptibilities can be straightforwardly expressed in terms of frequency integrals over the corresponding dynamical correlation functions.Google Scholar
  27. (25).
    An n-fold continued fraction with numerators b 0 …bn gt; 0 (c.f. refs. 17–19) has (n + 1) distinct poles. Numerically, we find that for large n these poles contain either negligibly small spectral weight or they are very densely clustered around a few frequency values, the actual excitation energies w v (q). This spurious splitting of the excitation energies (typically 1% or less) is a result of finite numerical accuracy and determines the limits of resolution of the CFE method. When broadened with a finite width ε = 0.03, our results are numerically stable (i.e. show very little n-dependence) between n = 5 and n = 200.Google Scholar
  28. (26).
    We have carefully re-derived the results of AA, ref. (14b), and believe that the left-hand side of their eq.(6) for SMF is in error by omission of an overall factor (2/NL). In all results shown in the present paper this missing factor has been included.Google Scholar
  29. (27).
    B. I. Shraiman and E. Siggia, Phys. Rev. Lett. 60, 740(1988); S. Trugman, Phys. Rev. 37, 1597 (1988).CrossRefADSMathSciNetGoogle Scholar
  30. (28).
    H. B. Schüttler and A. Fedro, J. Appl. Phys. 63, 4209(1988); P. Prelovsek, Phys. Lett. A126, 287(1988); J. Zaanen and A. M. Oles, Phys. Rev. B37, 9423 (1988).CrossRefADSGoogle Scholar
  31. (29).
    F. C. Zhang and T. M. Rice, Phys. Rev. B37, 3759 (1988).ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • C.-X. Chen
    • 1
  • H.-B. Schüttler
    • 1
  1. 1.Center for Simulational PhysicsUniversity of GeorgiaAthensUSA

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