Quantum-Monte-Carlo Studies of One- and Two-Dimensional Hubbard Models

  • R. Preuss
  • F. F. Assaad
  • A. Muramatsu
  • W. Hanke
Part of the NATO ASI Series book series (NSSB, volume 343)


Despite tremendous efforts, the question of whether two-dimensional repulsive Hubbard-type models have a superconducting phase, i. e. off-diagonal long-range order (ODLRO), is still unresolved. At present there is not even consensus on the symmetry channel in which superconductivity might occur! Therefore we present and numerically analyze two methods to detect superconductivity without any prior knowledge about the nature of the condensate and, in particular, of the symmetry of the underlying pair-pair correlation functions: flux quantization and the temperature derivative of the superfluid density. Both methods rely on generalizations of QMC algorithms to incorporate magnetic fields. Our data confirm the Kosterlitz-Thouless transition in the attractive case and rule out superconductivity in the quarter-filled repulsive one-band Hubbard model.


Hubbard Model Flux Quantization Luttinger Liquid Superfluid Density Large Lattice Size 
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  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.
    V.J. Emery, Phys. Rev. Lett. 58:2794 (1987).ADSCrossRefGoogle Scholar
  4. 4.
    For a review, see: E.Y. Loh and J.E. Gubernatis, Stable numerical simulations of models of interacting electrons in condensed-matter physics, in: “Modern Problems in Condensed Matter Sciences”, vol. 32, ed. W. Hanke and Y.V. Kopaev, North Holland (1992).Google Scholar
  5. 5.
    P.W. Anderson, Phys. Rev. Lett. 64:1839 (1990); Phys. Rev. Lett. 65:2306 (1990); Science 256:1526 (1992).ADSCrossRefGoogle Scholar
  6. 6.
    G. Dopf, A. Muramatsu and W. Hanke, Phys. Rev. Lett. 68:353 (1992).ADSCrossRefGoogle Scholar
  7. 7.
    G. Dopf, J. Wagner, P. Dieterich, A. Muramatsu and W. Hanke, Phys. Rev. Lett. 68:2082 (1992).ADSCrossRefGoogle Scholar
  8. 8.
    G. Dopf, A. Muramatsu and W. Hanke, Europhys. Lett. 17:559 (1992).ADSCrossRefGoogle Scholar
  9. 9.
    R.N. Silver, D.S. Sivia, and J.E. Gubernatis, Phys. Rev. B 41:2380 (1990), and references therein.ADSCrossRefGoogle Scholar
  10. 10.
    N. Byers and C.N. Yang, Phys. Rev. Lett. 7:46 (1961).ADSCrossRefGoogle Scholar
  11. 11.
    C.N. Yang, Reviews of Mod. Phys. 34:694 (1962).ADSCrossRefGoogle Scholar
  12. 12.
    R.T. Scalettar et al., Phys. Rev. Lett. 62:1407 (1989).ADSCrossRefGoogle Scholar
  13. 13.
    F.F. Assaad, W. Hanke and D.J. Scalapino, Phys. Rev. Lett. 71:1915 (1993).ADSCrossRefGoogle Scholar
  14. 14.
    J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6:1181 (1973).ADSCrossRefGoogle Scholar
  15. 15.
    D.R. Nelson and J.M. Kosterlitz, Phys. Rev. Lett. 39:1201 (1977).ADSCrossRefGoogle Scholar
  16. 16.
    A. Moreo and D.J. Scalapino, Phys. Rev. Lett. 66:946 (1991).ADSCrossRefGoogle Scholar
  17. 17.
    G. Dopf et al., Phys. Rev. Lett. 68:353 (1992), Phys. Rev. Lett. 68:2082 (1992), Europhys. Lett. 17:559 (1992).ADSCrossRefGoogle Scholar
  18. 18.
    F.F. Assaad, W. Hanke and D.J. Scalapino, to appear in Phys. Rev. B. Google Scholar
  19. 19.
    D.J. Scalapino, S.R. White and S.C. Zhang, Phys. Rev. Lett. 68:2830 (1992); Phys. Rev. B 47:7995 (1993).ADSCrossRefGoogle Scholar
  20. 20.
    E.H. Lieb and F.Y. Yu, Phys. Rev. Lett. 20:1445 (1965).ADSCrossRefGoogle Scholar
  21. 21.
    M. Takahashi, Prog. Theor. Phys. 43:1619 (1970).ADSCrossRefGoogle Scholar
  22. 22.
    S. Sorella and A. Parola, J. Phys. Cond. Matter 4:2589 (1992).CrossRefGoogle Scholar
  23. 23.
    R. Preuss et al., Würzburg preprint (1993).Google Scholar
  24. 24.
    H.J. Schulz, Int. J. Mod. Phys. B 5:57 (1991).ADSCrossRefGoogle Scholar
  25. 25.
    H. Frahm and V.E. Korepin, Phys. Rev. B 42:10553 (1990).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • R. Preuss
    • 1
  • F. F. Assaad
    • 1
  • A. Muramatsu
    • 1
  • W. Hanke
    • 1
  1. 1.Physikalisches InstitutUniversität WürzburgWürzburgGermany

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