Advertisement

Foundations of Physics

, Volume 30, Issue 12, pp 2033–2048 | Cite as

Variational Scheme for the Mott Transition

  • D. Baeriswyl
Article

Abstract

The Hubbard model is studied at half filling, using two complementary variational wave functions, the Gutzwiller ansatz for the metallic phase at small values of the interaction parameter U and its analog for the insulating phase at large values of U. The metallic phase is characterized by the Drude weight, which exhibits a jump at the critical point Uc. In the insulating phase the system behaves as a collection of dipoles which increase both in number and in size as U gets smaller. The two wave functions are able to describe the two asymptotic regimes (small and large values of U, respectively), but they can no longer be trusted in the region of the Mott transition (U≈Uc). More powerful methods are needed to study, for instance, the divergence of the electric susceptibility for U→Uc.

Keywords

Wave Function Interaction Parameter Powerful Method Hubbard Model Metallic Phase 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963).Google Scholar
  2. 2.
    M. C. Gutzwiller, Phys. Rev. 134, A923 (1964).Google Scholar
  3. 3.
    M. C. Gutzwiller, Phys. Rev. 137, A1726 (1965).Google Scholar
  4. 4.
    R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).Google Scholar
  5. 5.
    D. Vollhardt, Rev. Mod. Phys. 56, 99 (1984).Google Scholar
  6. 6.
    R. G. Parr, D. P. Craig, and I. G. Ross, J. Chem. Phys. 18, 1561 (1950).Google Scholar
  7. 7.
    R. G. Parr, J. Chem. Phys. 20, 1499 (1952).Google Scholar
  8. 8.
    R. Pariser and R. G. Parr, J. Chem. Phys. 21, 767 (1953).Google Scholar
  9. 9.
    J. A. Pople, Trans. Faraday Soc. 49, 1375 (1953).Google Scholar
  10. 10.
    P. W. Anderson, Phys. Rev. 115, 2 (1959).Google Scholar
  11. 11.
    J. Hubbard, Proc. Roy. Soc. (London) A 276, 238 (1963).Google Scholar
  12. 12.
    For a review see, D. Baeriswyl, D. K. Campbell, and S. Mazumdar, in Conjugated Conducting Polymers, H. Kiess, ed., Springer Series in Solid-State Sciences, Vol. 102 (Springer, New York, 1992), p. 7.Google Scholar
  13. 13.
    See, A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W. P. Su, Rev. Mod. Phys. 60, 781 (1988).Google Scholar
  14. 14.
    E. Jeckelmann and D. Baeriswyl, Synth. Met. 65, 211 (1994).Google Scholar
  15. 15.
    E. Jeckelmann, Phys. Rev. B 57, 11838 (1998).Google Scholar
  16. 16.
    J. Kanamori, Prog. Theor. Phys. 30, 275 (1963).Google Scholar
  17. 17.
    See, D. Vollhardt, N. Blümer, K. Held, M. Kollar, J. Schlipf, and M. Ulmke, Z. Phys. B 103, 283 (1997), and references therein.Google Scholar
  18. 18.
    N. F. Mott, Proc. Phys. Soc. 62, 416 (1949).Google Scholar
  19. 19.
    N. F. Mott, Metal-Insulator Transitions (Taylor & Francis, London, 1974).Google Scholar
  20. 20.
    J. Hubbard, Proc. Roy. Soc. (London) A 281, 401 (1964).Google Scholar
  21. 21.
    W. F. Brinkman and T. M. Rice, Phys. Rev. B 2, 4302 (1970).Google Scholar
  22. 22.
    W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989).Google Scholar
  23. 23.
    For a review see, A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).Google Scholar
  24. 24.
    J. Schlipf, M. Jarell, P. G. J. van Dongen, N. Blümer, S. Kehrein, Th. Pruschke, and D. Vollhardt, Phys. Rev. Lett. 82, 4890 (1999).Google Scholar
  25. 25.
    M. J. Rozenberg, R. Chitra, and G. Kotliar, Phys. Rev. Lett. 83, 3498 (1999).Google Scholar
  26. 26.
    W. Krauth, cond-mat/9908221.Google Scholar
  27. 27.
    G. Kotliar, E. Lange, and M. J. Rozenberg, cond-mat/0003016.Google Scholar
  28. 28.
    P. W. Anderson, in Frontiers and Borderlines in Many-Particle Physics, R. A. Broglia and J. R. Schrieffer, eds. (North Holland, Amsterdam, 1988), p. 1.Google Scholar
  29. 29.
    D. J. Scalapino, Phys. Rep. 250, 329 (1995).Google Scholar
  30. 30.
    S. Zhang, J. Carlson, and J. E. Gubernatis, Phys. Rev. Lett. 78, 4486 (1997).Google Scholar
  31. 31.
    D. Zanchi and H. J. Schulz, Phys. Rev. B 61, 13609 (2000).Google Scholar
  32. 32.
    C. J. Halboth and W. Metzner, Phys. Rev. B 61, 7364 (2000).Google Scholar
  33. 33.
    For a recent review see, J. Orenstein and A. J. Millis, Science 288, 468 (2000).Google Scholar
  34. 34.
    For an early review see, R. Micnas, J. Ranninger, and S. Robaskiewicz, Rev. Mod. Phys. 62, 113 (1990).Google Scholar
  35. 35.
    M. Randeria, in Bose_Einstein Condensation, A. Griffin et al., eds. (Cambridge University Press, Cambridge, 1995).Google Scholar
  36. 36.
    E. H. Lieb, Phys. Rev. Lett. 62, 1201 (1989); Erratum ibid., 1927 (1989).Google Scholar
  37. 37.
    R. M. Wilcox, J. Math. Phys. 8, 962 (1967).Google Scholar
  38. 38.
    D. Baeriswyl, Proc. Int. Conf. on Nonlinearity in Condensed Matter, Springer Series in Solid-State Sciences, Vol. 69 (Springer, New York, 1987), p. 183.Google Scholar
  39. 39.
    H. Otsuka, J. Phys. Soc. Jpn. 61, 1645 (1992).Google Scholar
  40. 40.
    M. Dzierzawa, D. Baeriswyl, and M. Di Stasio, Phys. Rev. B 51, 1993 (1995).Google Scholar
  41. 41.
    F. Gebhard and A. E. Ruckenstein, Phys. Rev. Lett. 68, 244 (1992).Google Scholar
  42. 42.
    W. Kohn, Phys. Rev. 133, A171 (1964).Google Scholar
  43. 43.
    B. S. Shastry and B. Sutherland, Phys. Rev. Lett. 65, 243 (1990).Google Scholar
  44. 44.
    A. J. Millis and S. N. Coppersmith, Phys. Rev. B 43, 13770 (1991).Google Scholar
  45. 45.
    M. Dzierzawa, D. Baeriswyl, and L.M. Martelo, Helv. Phys. Acta 70, 124 (1997).Google Scholar
  46. 46.
    P. W. Anderson, Basic Notions of Condensed Matter Physics (Benjamin/Cummings, Menlo Park, California, 1984).Google Scholar
  47. 47.
    D. Baeriswyl, C. Gros, and T. M. Rice, Phys. Rev. B 35, 8391 (1987).Google Scholar
  48. 48.
    D. Pines and P. Nozières, The Theory of Quantum Liquids (W. A. Benjamin, New York, 1966).Google Scholar
  49. 49.
    J. C. Slater, Phys. Rev. 82, 538 (1951).Google Scholar
  50. 50.
    H. Yokoyama and H. Shiba, J. Phys. Soc. Japan 56, 3582 (1987).Google Scholar
  51. 51.
    L. M. Martelo, M. Dzierzawa, L. Siffert, and D. Baeriswyl, Z. Phys. B 103, 335 (1997).Google Scholar
  52. 52.
    W. Metzner and D. Vollhardt, Phys. Rev. Lett. 59, 121 (1987).Google Scholar
  53. 53.
    H. Yokoyama and H. Shiba, J. Phys. Soc. Japan 56, 1490 (1987).Google Scholar
  54. 54.
    C. Gros, R. Joynt and T. M. Rice, Phys. Rev. B 36, 381 (1987).Google Scholar
  55. 55.
    F. Gebhard and A. Girndt, Z. Phys. B 93, 455 (1994).Google Scholar
  56. 56.
    C. K. Majumdar and D. K. Ghosh, J. Math. Phys. 10, 1388 (1969).Google Scholar
  57. 57.
    F. D. M. Haldane, Phys. Rev. Lett. 60, 635 (1988).Google Scholar
  58. 58.
    B. S. Shastry, Phys. Rev. Lett. 60, 639 (1988).Google Scholar
  59. 59.
    T. Kennedy, E. H. Lieb, and B. S. Shastry, Phys. Rev. Lett. 61, 2582 (1988).Google Scholar
  60. 60.
    C. Aebischer, D. Baeriswyl, and R. M. Noack, cond-mat/0006354.Google Scholar
  61. 61.
    N. F. Mott, Philos. Mag. 26, 1015 (1972).Google Scholar
  62. 62.
    C. Aebischer, D. Baeriswyl, and R. M. Noack, unpublished.Google Scholar
  63. 63.
    C. A. Stafford and A. J. Millis, Phys. Rev. B 48, 1409 (1993).Google Scholar
  64. 64.
    S. Sorella and E. Tosatti, Europhys. Lett. 19, 699 (1992).Google Scholar
  65. 65.
    M. Capone, L. Capriotti, F. Becca, and S. Caprara, cond-mat/0006437.Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • D. Baeriswyl
    • 1
  1. 1.Institut de Physique ThéoriqueUniversité de FribourgFribourgSwitzerland

Personalised recommendations