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Physica B Condensed Matter

The breakdown of Fermi liquid theory in the Hubbard model

David M. Edwards, John Hertz

Published Apr 1, 1990• 34 citations
Publisher
DOI
10.1016/0921-4526(90)90259-w

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The breakdown of Fermi liquid theory in the Hubbard model: II

David M. Edwards

For pt.I see Physics B, vol.163, p.527 (1990). An exact diagrammatic analysis of the electron self-energy in the Hubbard and related models is given within the local approximation. Contact is made with recent work for dimension d= infinity where the local approximation becomes exact. It is shown that the approximate method of paper I of the series may be fitted into the new framework and yields sensible results for the Anderson impurity model. This lends weight to the prediction of I that for paramagnetic solutions of the Hubbard model Fermi liquid behaviour breaks down in a whole region of the T=0 phase diagram, not just for a half-filled band where the Mott transition occurs.

Journal of Physics Condensed Matter•Jan 11, 1993•16 citations
We reexamine the Brandt-Mielsch solution of the Falicov-Kimball model in infinite dimensions, to elucidate the mechanism for the breakdown of Fermi-liquid theory in this model. We find that this breakdown is due to the pinning of the chemical potential at the localized particle level. When this pinning does not occur, Fermi-liquid theory is restored. Using a Lorentzian density of states, we obtain analytic expressions for spectral densities and local response functions. These expressions give new insights into the formation of upper and lower Hubbard bands, the metal-insulator transition, the softening of the collective modes, and the infrared singularities of this model.
For pt.I see Physics B, vol.163, p.527 (1990). An exact diagrammatic analysis of the electron self-energy in the Hubbard and related models is given within the local approximation. Contact is made with recent work for dimension d= infinity where the local approximation becomes exact. It is shown that the approximate method of paper I of the series may be fitted into the new framework and yields sensible results for the Anderson impurity model. This lends weight to the prediction of I that for paramagnetic solutions of the Hubbard model Fermi liquid behaviour breaks down in a whole region of the T=0 phase diagram, not just for a half-filled band where the Mott transition occurs.