Advertisement

Hidden Symmetry of Strongly Correlated Fermons

  • D. Foerster
  • N. Schopohl
Chapter
  • 382 Downloads
Part of the NATO ASI Series book series (NSSB, volume 343)

Abstract

The Hubbard Hamiltonian at large U has an extra conserved charge.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    For a recent review: P. Fulde in “Electron Correlations in Molecules and Solids”, Springer Series in Solid State Sciences, vol. 100, (Springer Berlin 1992).Google Scholar
  2. [2]
    We use notation such that σ = ↑, ↓ is the spin, x and y specify sites in the d-dimensional lattice A, and h x,y is the hopping probability from site x to \( \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{c} \) and c yσ are standard fermion creation and annihilation operators, \( {n_{x\sigma }} = c_{x\sigma }^ + {c_{x\sigma }} \) is the local occupation number of one particle states with spin σ, and \( {D_x} = {n_{x \uparrow }}{n_{x \uparrow }} \) is the double occupancy at site x.Google Scholar
  3. [3]
    For example: K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975).ADSCrossRefGoogle Scholar
  4. [4]
    A.B. Harris and R.V. Lange, Phys. Rev. 157, 295 (1967)ADSCrossRefGoogle Scholar
  5. A.H. MacDonald, S.M. Girvin und D. Yoshioka, Phys. Rev. B37, 9753 (1988).ADSGoogle Scholar
  6. [5]
    Several authors have recently constructed upper and lower bounds on the ground state energy of such operators that coincide at half filling: U. Brandt and A. Giesekus, Phys. Rev. Lett. 68, 2468 (1992)CrossRefGoogle Scholar
  7. A. Mielke, J. Phys. A 25, 6507 (1992); Hal Tasaki, Phys. Rev. Lett. 70, 3303(1993)MathSciNetADSCrossRefGoogle Scholar
  8. R. Strack and D. Vollhardt, Phys. Rev. Lett. 70, 2637 (1993)ADSCrossRefGoogle Scholar
  9. R. Strack, Phys. Rev. Lett. 70, 833 (1993).ADSCrossRefGoogle Scholar
  10. [6]
    H. Shiba, Prog. Theor. Phys. 48, 2171 (1972)ADSCrossRefGoogle Scholar
  11. S. Ostlund, Phys. Rev. Lett. 69, 1695 (1992)ADSCrossRefGoogle Scholar
  12. C.N. Yang, Phys. Lett. A161, 292 (1992).ADSGoogle Scholar
  13. [7]
    M. Noga, Czechoslovak Journal of Physics 42, 823 (1992).ADSzbMATHCrossRefGoogle Scholar
  14. [9]
    The bare creation and anihilation operators, \( c_{x\sigma }^ + \) and c xσ, change under the canonical transformation generated by S into creation-and anihilitation operators of quasi particles: \( \gamma _{x\sigma }^ + = {e^S}c_{x\sigma }^ + {e^{ - S}} = c_{x\sigma }^ + + \left[ {S,c_{x\sigma }^ + } \right] + \ldots \) and γxσ = e s c xσ e s = c xσ + [S, c xσ] +.... Note that the higher order manybody terms \( \left[ {S,c_{x\sigma }^{\left( {{\rm{ + }}} \right)}} \right] + \ldots \)+... contribute to the incoherent background of spectral functions, and cannot be omitted.Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • D. Foerster
    • 1
  • N. Schopohl
    • 2
  1. 1.Service National des Champs IntensesC.N.R.S.Grenoble CedexFrance
  2. 2.Centre de Recherches sur les Tres Basses TemperaturesC.N.R.S.Grenoble CedexFrance

Personalised recommendations