Exact Results on a Supersymmetric Extended Hubbard Model

  • Fabian H. L. Eßler
  • Vladimir E. Korepin
Part of the NATO ASI Series book series (NSSB, volume 343)


The two most promising models of correlated electrons in relation with high-T c superconductivity are the Hubbard and t-J models. Both are related to the isotropic spin-1/2 Heisenberg antiferromagnet (XXX model): the Hubbard model via the U → ∞limit and the t-J model by tuning the chemical potential to half-filling. In one dimension the Hubbard model, the t-Jmodel at the supersymmetric point J = ±2t, and the Heisenberg model are integrable and can be solved exactly by means of the Bethe Ansatz[1–4]. These exact solutions first of all provide checks for other methods employed to study two-dimensional models, they give intuition about the effects of strong correlations, and may even be of direct relevance for the two-dimensional models, which are believed to share important features with their one-dimensional analogs[5]. The XXX model and the supersymmetric t-Jmodel (st-J) have another interesting common feature: they are maximally symmetric in the sense that their hamiltonians are invariant under all global unitary rotations of the bases of their respective Hilbert spaces. Let us consider a lattice of length L with periodic boundary conditions.


Hubbard Model Reduce Density Matrix Tensor Product Space Hubbard Interaction Lower Weight State 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. Bethe, Z. Phys. 71 (1931) 205.ADSCrossRefGoogle Scholar
  2. [2]
    E.H. Lieb, F.Y. Wu, Phys. Rev. Lett. 20 (1968) 1445.ADSCrossRefGoogle Scholar
  3. [3]
    B. Sutherland, Phys. Rev. B12 (1975) 3795.ADSGoogle Scholar
  4. [4]
    P. Schlottmann, Phys. Rev. B36 (1987) 5177.ADSGoogle Scholar
  5. [5]
    P.W. Anderson, Science 235 (1987) 1196.ADSCrossRefGoogle Scholar
  6. [6]
    A. Montorsi, M. Rasetti, A.I. Solomon, Int. J. Mod. Phys. B3 (1989) 247.MathSciNetADSGoogle Scholar
  7. [7]
    J.E. Hirsch, Physica C158 (1990) 326.ADSGoogle Scholar
  8. [8]
    R.Z. Bariev, A. Klümper, A. Schadschneider, J. Zittartz, J. Physics A26 (1993) 1249.ADSGoogle Scholar
  9. [9]
    K.A. Penson, M. Kolb, Phys. Rev. B33 (1986) 1663.ADSGoogle Scholar
  10. [10]
    M. Kolb, K.A. Penson, J. Stat. Phys. 44 (1986) 129.ADSCrossRefGoogle Scholar
  11. [11]
    I. Affleck, J.B. Marston, J. Physics C21 (1988) 2511.ADSGoogle Scholar
  12. [12]
    J. Hubbard, Proc. Roy. Soc. 276 (1963) 238.ADSCrossRefGoogle Scholar
  13. [13]
    D.K. Campbell, theses proceedings.Google Scholar
  14. [14]
    D. Vollhardt, theses proceedings.Google Scholar
  15. [15]
    F.H.L. Eßler, V.E. Korepin, K. Schoutens, Phys. Rev. Lett. 68 (1992) 2960.MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. [16]
    C.N. Yang, Phys. Rev. Lett. 63 (1989) 2144.ADSCrossRefGoogle Scholar
  17. [17]
    P.A. Bares, G. Blatter, M. Ogata, Phys. Rev. B44 (1991) 130.ADSGoogle Scholar
  18. [18]
    F.H.L. Eßler, V.E. Korepin, K. Schoutens, Phys. Rev. Lett. 70 (1993) 73.ADSCrossRefGoogle Scholar
  19. [19]
    C.N. Yang, Rev. Mod. Phys. 34 (1962) 694.ADSCrossRefGoogle Scholar
  20. [20]
    G. Sewell, J. Stat. Phys. 61 (1990) 415.MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    K.P. Sinha, Solid State Comm. 79 (1991) 735 and references therein.ADSCrossRefGoogle Scholar
  22. [22]
    B.N. Ganguly, U.N. Upadhyaya, K.P. Sinha, Phys. Rev. 146 (1966) 317.ADSCrossRefGoogle Scholar
  23. [23]
    R. Friedberg, T.D. Lee, Phys. Lett. 138A (1989) 423.ADSGoogle Scholar
  24. [24]
    R. Friedberg, T.D. Lee, Phys. Rev. B40 (1989) 6745.ADSGoogle Scholar
  25. [25]
    R. Friedberg, T.D. Lee, H.C. Ren, Phys. Lett. 152A (1991) 417.ADSGoogle Scholar
  26. [26]
    R. Friedberg, T.D. Lee, H.C. Ren, Phys. Lett. 152A (1991) 423.ADSGoogle Scholar
  27. [27]
    A.A. Belavin, A.A. Polyakov, A.B. Zamolodchikov, Nucl. Phys. B241 (1984) 333.MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    H. Frahm, V.E. Korepin, Phys. Rev. B42 (1990) 10533.Google Scholar
  29. [29]
    H. Frahm, V.E. Korepin, Phys. Rev. B43 (1991) 5653.ADSGoogle Scholar
  30. [30]
    I. Affleck, Phys. Rev. Lett. 56 (1986) 746.MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    H.W.J. Blöte, J.L. Cardy, M.P. Nightingale, Phys. Rev. Lett. 56 (1986) 742.ADSCrossRefGoogle Scholar
  32. [32]
    J.L. Cardy, Nucl. Phys. B270 (1986) 186.MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    N. Kawakami, S.K. Yang, J. Physics C3 (1991) 5983.Google Scholar
  34. [34]
    N. Kawakami, S.K. Yang, Phys. Rev. Lett. 67 (1990) 2309.MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    P.P. Kulish, J. Soviet Math. 35 (1985) 2648.CrossRefGoogle Scholar
  36. [36]
    F.H.L.Eßler, V.E. Korepin, K. Schoutens, preprint ITP-92-57.Google Scholar
  37. [37]
    F.H.L.Eßler, V.E. Korepin, preprint ITP-93-15.Google Scholar
  38. [38]
    C.K. Lai, J. Math. Phys. 15 (1974) 1675.ADSCrossRefGoogle Scholar
  39. [39]
    F.H.L. Eßler, V.E. Korepin, Phys. Rev. B46 (1992) 9147.ADSGoogle Scholar
  40. [40]
    C.N. Yang, C.P. Yang, J. Math. Phys. 10 (1969) 1115.ADSzbMATHCrossRefGoogle Scholar
  41. [41]
    M. Takahashi, Prog. Theor. Phys. 46 (1971) 401.ADSCrossRefGoogle Scholar
  42. [42]
    A. Förster, M. Karowski, Nucl. Phys. B396 (1993) 611.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Fabian H. L. Eßler
    • 1
  • Vladimir E. Korepin
    • 2
  1. 1.Physikalisches InstitutUniversität BonnBonnDeutschland
  2. 2.Institute for Theoretical PhysicsState University of New York at Stony BrookStony BrookUSA

Personalised recommendations