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The Mott-Hubbard metal-insulator transition in the limit of large dimensions—Insights and outlook

  • Stefan Kehrein
Interactions and Disorder
Part of the Advances in Solid State Physics book series (ASSP, volume 39)

Abstract

The Mott-Hubbard metal-insulator transition is one of the classical and fundamental problems in solid-state physics. A new theoretical approach has become possible within the limit of large dimensions (dynamical mean field theory). Numerous analytical and numerical techniques have since addressed the question of the d=∞ Mott-Hubbard transition. However, the nature of this transition is still controversial. In this paper a brief account is presented of some of the recent results regarding the d=∞ Mott-Hubbard transition.

Keywords

Hubbard Model Bethe Lattice Coexistence Region Exact Diagonalization Numerical Renormalization Group 
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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Bibliography

  1. [1]
    J. H. de Boer and E. J. W. Verwey, Proc. Phys. Soc. London, Ser. A 49, 59 (1937).CrossRefADSGoogle Scholar
  2. [2]
    N. F. Mott, Proc. Phys. Soc. London, Ser. A 49, 72 (1937).CrossRefADSGoogle Scholar
  3. [3]
    N. F. Mott, Metal-Insulator Transitions, 2nd edition, (Taylor and Francis, London 1990).Google Scholar
  4. [4]
    F. Gebhard, The Mott Metal-Insulator Transition, (Springer, Berlin 1997).Google Scholar
  5. [5]
    M. Imada, A. Fujimori and Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998).CrossRefADSGoogle Scholar
  6. [6]
    D. B. McWhan, J. P. Remeika, T. M. Rice, W. F. Brinkman, J. P. Maita and A. Menth, Phys. Rev. Lett. 27, 941 (1971).CrossRefADSGoogle Scholar
  7. [7]
    J. Hubbard, Proc. Roy. Soc. London Ser. A 276, 238 (1963); ibid. J. Hubbard, Proc. Roy. Soc. London Ser. A 277, 237 (1963).ADSCrossRefGoogle Scholar
  8. [8]
    M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963).CrossRefADSGoogle Scholar
  9. [9]
    J. Kanamori, Prog. Theor. Phys. 30, 275 (1963).MATHCrossRefADSGoogle Scholar
  10. [10]
    J. Hubbard, Proc. Roy. Soc. London 281, 401 (1964).ADSCrossRefGoogle Scholar
  11. [11]
    W. F. Brinkman and T. M. Rice, Phys. Rev. B 2, 4302 (1970).CrossRefADSGoogle Scholar
  12. [12]
    W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989).CrossRefADSGoogle Scholar
  13. [13]
    A. Georges, G. Kotliar, W. Krauth and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).CrossRefADSMathSciNetGoogle Scholar
  14. [14]
    E. Müller-Hartmann, Z. Phys. B 74, 507 (1989).CrossRefADSGoogle Scholar
  15. [15]
    E. Müller-Hartmann, Z. Phys. B 76, 211 (1989).CrossRefADSGoogle Scholar
  16. [16]
    A. Georges and W. Krauth, Phys. Rev. B 48, 7167 (1993).CrossRefADSGoogle Scholar
  17. [17]
    A. Georges and G. Kotliar, Phys. Rev. B 45, 6479 (1992).CrossRefADSGoogle Scholar
  18. [18]
    G. Moeller, Q. Si, G. Kotliar, M. J. Rozenberg, and D. S. Fisher, Phys. Rev. Lett. 74, 2082 (1995).CrossRefADSGoogle Scholar
  19. [19]
    S. Kehrein, Phys. Rev. Lett. 81, 3912 (1998).CrossRefADSGoogle Scholar
  20. [20]
    W. Hofstetter and S. Kehrein, Preprint cond-mat/9812427, to appear in Phys. Rev. B.Google Scholar
  21. [21]
    J. Schlipf, M. Jarrell, P. G. J. van Dongen, N. Blümer, S. Kehrein, Th. Pruschke and D. Vollhardt, Preprint cond-mat/9902267.Google Scholar
  22. [22]
    M. J. Rozenberg, G. Kotliar, H. Kajueter, G. A. Thomas D. H. Rapkine, J. M. Honig and P. Metcalf, Phys. Rev. Lett. 75, 105 (1995).CrossRefADSGoogle Scholar
  23. [23]
    W. Hofstetter, private communication.Google Scholar
  24. [24]
    K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975).CrossRefADSGoogle Scholar
  25. [25]
    R. Bulla, Preprint cond-mat/9902290.Google Scholar
  26. [26]
    O. Sakai and Y. Kuramoto, Solid State Commun. 89, 307 (1994).CrossRefADSGoogle Scholar
  27. [27]
    R. M. Noack and F. Gebhard, Phys. Rev. Lett. 82, 1915 (1999).CrossRefADSGoogle Scholar
  28. [28]
    P. Nozières, Eur. Phys. J. B 6, 447 (1998).CrossRefADSGoogle Scholar
  29. [29]
    D. E. Logan and P. Nozières, Phil. Trans. R. Soc. London A356, 249 (1998).CrossRefADSGoogle Scholar
  30. [30]
    P. Majumdar and H. R. Krishnamurthy, Phys. Rev. B. 18, 4945 (1978).CrossRefGoogle Scholar
  31. [32]
    W. Bao, C. Broholm, G. Aeppli, P.Dai, J. M. Honig and P. Metcalf, Phys. Rev. Lett. 78, 507 (1997).CrossRefADSGoogle Scholar
  32. [33]
    S. Yu. Ezhov, V. I. Anisimov, D. I. Khmoskii and G. A. Sawatzky, Preprint condmat/9901229.Google Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH 1999

Authors and Affiliations

  • Stefan Kehrein
    • 1
  1. 1.Department of PhysicsHarvard UniversityCambridgeUSA

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