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The Phase Diagram of the One-Dimensional Extended Hubbard Model

  • H. Q. Lin
  • E. R. Gagliano
  • D. K. Campbell
  • E. H. Fradkin
  • J. E. Gubernatis
Chapter
Part of the NATO ASI Series book series (NSSB, volume 343)

Abstract

For a wide range of its three parameters — the Coulomb interactions U and V and the band filling ρ — we obtain the phase diagram of one-dimensional, “conventional” extended Hubbard model by combining previously known weak-coupling results with strong coupling perturbation theory, quantum Monte Carlo (QMC), and exact diagonalization) simulations. Our results establish the existence of a variety of phases, including several not predicted by weak coupling arguments. We delineate, for all ρ, the regions of the U, V parameter plane in which the model exhibits the “Luttinger Liquid” behavior expected for a strongly correlated, one-dimensional metal. In other regions, we establish the nature of the dominant fluctuations and, if relevant, the broken symmetry ground states. We evaluate the charge-charge, spin-spin, and superconducting pairing susceptibilities and correlation functions and calculate the charge correlation exponent, K ρ. Our results are generally consistent with, but substantially extend, previous analyses based on QMC, exact diagonalization, and renormalization group studies.

Keywords

Hubbard Model Charge Density Wave Spin Density Wave Exact Diagonalization Luttinger Liquid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    For an overview, written in the specific context of conducting polymers, that presents a discussion of the broader context of electron-electron (and electron-phonon) interactions in novel electronic materials in reduced dimensions, see D. Baeriswyl, D. K. Campbell, and S. Mazumdar pp. 7-134 in Conjugated Conducting Polymers, H. Kiess, ed. (Springer, 1992).Google Scholar
  2. 2.
    W. P. Su and J. R. Schrieffer, Phys. Rev. Lett. 46, 735 (1981).ADSCrossRefGoogle Scholar
  3. 3.
    See, e. g., S. Mazumdar, H. Q. Lin, and D. K. Campbell, pp. 221-229 in Organic Superconductivity, V. Z. Kresin and W. A. Little, eds., (Plenum, 1990), and references therein.Google Scholar
  4. 4.
    D. Poilblanc, T. Ziman, J. Bellisard, F. Mila, and G. Montambaux, Europhys. Lett. 22, 537 (1993)ADSCrossRefGoogle Scholar
  5. 5.
    V. J. Emery, pp. 247–303 in Highly Conducting One-Dimensional Solids, edited by J. T. Devreese et al. (Plenum, New York, 1979).CrossRefGoogle Scholar
  6. 6.
    J. Solyom, Adv. in Physics 28, 201 (1979).ADSCrossRefGoogle Scholar
  7. 7.
    B. Fourcade and G. Sproken, Phys. Rev. B 29, 5089 (1984).ADSCrossRefGoogle Scholar
  8. 8.
    A. Luther and I. Peschel, Phys. Rev. B 9, 2911 (1974)ADSCrossRefGoogle Scholar
  9. D. C. Mattis, J. Math. Phys. 15, 609 (1974)ADSCrossRefGoogle Scholar
  10. J. Cannon and E. Fradkin, Phys. Rev. B 41, 9435 (1990)ADSCrossRefGoogle Scholar
  11. J. Voit, Phys. Rev. B 45, 4027 (1992).ADSCrossRefGoogle Scholar
  12. 9.
    L. Milas del Bosch and L. M. Falicov, Phys. Rev. B 37, 6073 (1988)ADSCrossRefGoogle Scholar
  13. B. Fourcade and G. Sproken, Phys. Rev. B 29, 5096 (1984).ADSCrossRefGoogle Scholar
  14. 10.
    J. E. Hirsch, Phys. Rev. Lett. 53, 2327 (1984).ADSCrossRefGoogle Scholar
  15. 11.
    J. E. Hirsch and D. J. Scalapino, Phys. Rev. B 27, 7169 (1983); 29, 5554 (1984).ADSCrossRefGoogle Scholar
  16. 12.
    H. Q. Lin and J. E. Hirsch, Phys. Rev. B 33, 8155 (1986).ADSCrossRefGoogle Scholar
  17. 13.
    J. Cannon, R. Scallettar, and E. Fradkin, Phys. Rev. B 44, 5995 (1991).ADSCrossRefGoogle Scholar
  18. 14.
    V. J. Emery, Phys. Rev. B 14, 2989 (1976)ADSCrossRefGoogle Scholar
  19. see also M. Fowler, Phys. Rev. B. 17, 2989 (1978)ADSCrossRefGoogle Scholar
  20. K. B. Efetov and A. I. Larkin, Sov. Phys. JETP, 42, 390 (1976).ADSGoogle Scholar
  21. 15.
    See P. J. van Dongen, these proceedings (The Hubbard Model: Proceedings of the 1993 NATO ARW on “The Physics and Mathematical Physics of the Hubbard Model”, edited by D. Baeriswyl et al. (Plenum, 1995).)Google Scholar
  22. 16.
    F. Mila and X. Zotos, Europhys. Lett. 24, 133 (1993).ADSCrossRefGoogle Scholar
  23. 17.
    F. D. M. Haldane, Phys. Rev. Lett. 45, 1358 (1980)MathSciNetADSCrossRefGoogle Scholar
  24. F. D. M. Haldane, J. Phys. C 14, 2585 (1981).ADSCrossRefGoogle Scholar
  25. 18.
    For a history of many-body problems in one dimension from a perspective especially relevant for this article, see V. J. Emery, pp. 166-198 in Correlated Electron Systems, edited by V. J. Emery, (World Scientific, 1993), and references therein.Google Scholar
  26. 19.
    H. J. Schulz, Phys. Rev. Lett. 64, 2831 (1990)ADSCrossRefGoogle Scholar
  27. H. J. Schulz, Int. J. Mod. Phys. B 5, 57 (1991).ADSCrossRefGoogle Scholar
  28. 20.
    H. Frahm and V. E. Korepin, Phys. Rev. B 42, 10553 (1990); Phys. Rev. B 43, 5643 (1991).ADSCrossRefGoogle Scholar
  29. 21.
    N. Kawakami and S. K. Yang, Phys. Rev. Lett. 65, 2309 (1990); Phys. Lett. A 148, 359 (1990)MathSciNetADSzbMATHCrossRefGoogle Scholar
  30. J. M. P. Carmelo, P. Horsch and A. A. Ovchinnikov, Phys. Rev. B 46, 14728 (1992).ADSCrossRefGoogle Scholar
  31. 22.
    N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).ADSCrossRefGoogle Scholar
  32. 23.
    H. Q. Lin, E. R. Gagliano, D. K. Campbell, E. H. Fradkin, and J. E. Gubernatis, to be published in Phys. Rev. B. Google Scholar
  33. 24.
    J. E. Hirsch, D. J. Scalapino, R. L. Sugar, and R. Blankenbecler, Phys. Rev. B. 26, 5033 (1982).ADSCrossRefGoogle Scholar
  34. 25.
    H. Q. Lin and J. E. Gubernatis, Comput. Phys. 7, 400 (1993)Google Scholar
  35. see also E. R. Gagliano et ai, Phys. Rev. B 34, 1677 (1986).ADSCrossRefGoogle Scholar
  36. 26.
    C.A. Stafford, A.J. Millis, and B.S. Shastry, Phys. Rev. B 43, 13660 (1991).ADSCrossRefGoogle Scholar
  37. 27.
    R.M. Fye, M.J. Martins, D.J. Scalapino, J. Wagner, and W. Hanke, Phys. Rev. B 44, 6909 (1991).ADSCrossRefGoogle Scholar
  38. 28.
    G. Gomez-Santos, Phys. Rev. Lett. 70, 3780 (1993); see also his contribution to these proceedings.ADSCrossRefGoogle Scholar
  39. 29.
    K. Penc, private communication; K. Penc and F. Mila, Phys. Rev. B, to be published.Google Scholar
  40. 30.
    K. Sano and Y. Ono, preprint, to be published in J. Phys. Soc. Japan.Google Scholar
  41. 31.
    Dandan Guo, S. Mazumdar, S. N. Dixit, F. Kajzar, F. Jarka, Y. Kawabe, and N. Peyghambrian, Phys. Rev. B 48, 1433 (1993).ADSCrossRefGoogle Scholar
  42. 32.
    Many quasi-one-dimensional compounds show this 4k F feature in diffuse X-ray scattering. For more details see, J.P. Pouget, p. 87 in in Highly Conducting Quasi-One-Dimensional Crystal Semiconductors and Semimetals (Pergamon, New York, 1988).Google Scholar
  43. 33.
    S. Mazumdar, D. Toussaint, and K.-C. Ung, Phys. Rev. Lett. 73, 2603 (1994).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • H. Q. Lin
    • 1
  • E. R. Gagliano
    • 1
    • 2
  • D. K. Campbell
    • 1
  • E. H. Fradkin
    • 1
  • J. E. Gubernatis
    • 3
  1. 1.Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Centro Atomico BarilocheBarilocheArgentina
  3. 3.Theoretical Division, MS B 262Los Alamos National LaboratoryLos AlamosUSA

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