Abstract
Recently it was shown that the theory of systems of correlated fermions on a lattice is greatly simplified in the limit of high dimensions as compared to lattice systems of dimensions 2 or 3 or to isotropic systems. We discuss here the implications of the limit of high dimensions on the single particle propagator of the Hubbard model. It is shown that all the typical Fermi liquid features are retained at high dimensions. Some exact results are obtained for infinite dimension: the shape of the Fermi surface as well as the density of states at the Fermi surface are not renormalized at all by the Coulomb interaction as long as the symmetry of the system is not broken. The self-consistent weak coupling theory is cast into a form which is solved numerically with very little effort.
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Research performed within the program of the Sonderforschungs-bereich 341 supported by the Deutsche Forschungsgemeinschaft
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Müller-Hartmann, E. The Hubbard model at high dimensions: some exact results and weak coupling theory. Z. Physik B - Condensed Matter 76, 211–217 (1989). https://doi.org/10.1007/BF01312686
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DOI: https://doi.org/10.1007/BF01312686