Drude Weight and f-Sum Rule of the Hubbard Model at Strong Coupling

  • Peter Horsch
  • Walter Stephan
Part of the NATO ASI Series book series (NSSB, volume 343)


The motion of holes in the two-dimensional single-band Hubbard and t-J model is intimately related to the dynamics of holes or electrons doped in copper-oxide based superconductors.1,2 The latter model is supposed to describe the low-energy physics in a partially filled Hubbard band. Transitions accross the Hubbard gap are integrated out and give rise to the effective antiferromagnetic Heisenberg interaction among the (Cu)-spins in the t-J Hamiltonian. The optical conductivity3–5 and the Drude weight6–10 of the 2D Hubbard and t-J models have been studied recently by several authors using Lanczos diagonalization techniques. There exist also studies for two-band models which include explicitely Cu and 0 orbitals in the unit cell.11 Characteristic for the Hubbard model is a fast decrease of absorption into the upper Hubbard band upon doping.5 The spectral weight is transfered to the lower Hubbard band, and gives rise to a Drude peak at zero energy (in the absence of impurities) and in the 2D case to a rapid growth of a broad absorption band at finite frequency. This has led several authors to suggest that the anomalous midinfrared absorption observed in all doped copper oxides12,13 may have a natural explanation in this framework in the broad absorption band resulting from the strong coupling of the charge carriers to the spin degrees of freedom4,5. The Bethe Ansatz soluble one-dimensional models appear to be different due to spin-charge decoupling. As a consequence the dissipative part of their spectra is very small3,5,9 and almost all spectral weight is in the Drude peak14–18.


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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Peter Horsch
    • 1
  • Walter Stephan
    • 2
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgartFed. Rep. Germany
  2. 2.King’s College LondonStrand, LondonUK

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