Cumulant expansion of the periodic Anderson model in infinite dimensions

@article{Foglio1997CumulantEO,
  title={Cumulant expansion of the periodic Anderson model in infinite dimensions},
  author={Mario E. Foglio and M. S. Figueira},
  journal={Journal of Physics A},
  year={1997},
  volume={30},
  pages={7879-7894}
}
The diagrammatic cumulant expansion for the periodic Anderson model with infinite Coulomb repulsion is considered here for an hypercubic lattice of infinite dimension . The nearest neighbour hopping of the uncorrelated electrons is described exactly by a conduction band, while two different models of hybridization are treated as a perturbation. The same type of simplifications obtained by Metzner for the cumulant expansion of the Hubbard model in the limit of , are also shown to be valid for… 
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References

SHOWING 1-10 OF 24 REFERENCES
Cumulant expansion of the periodic Anderson model: General derivation.
TLDR
The rules for the diagrammatic calculation of the grand canonical potential and of the Green's functions for the general model are given and only connected diagrams appear in those calculations and the lattice sums are unrestricted.
The cumulant expansion of the periodic Anderson model; completeness and the -derivable approximation
The approximate Green's functions of the localized electrons, obtained by the cumulant expansion of the periodic Anderson model in the limit of infinite Coulomb repulsion, do not satisfy completeness
Periodic Anderson model in infinite dimensions.
The symmetric periodic Anderson model is studied in the limit of infinite spatial dimensions within an essentially exact quantum Monte Carlo method. The single-particle spectral function develops a
Tight-binding treatment of the Hubbard model in infinite dimensions.
  • Craco, Gusmão
  • Physics, Medicine
    Physical review. B, Condensed matter
  • 1996
TLDR
The Hubbard model is discussed by means of a perturbative expansion of the one-particle Green’s function around the atomic limit, allowing a formal resummation that reproduces a previously proposed mapping to a single-site mean-field problem.
Correlated fermions on a lattice in high dimensions
The limit of infinite dimension of the Hubbard model was recently introduced by Metzner and Vollhardt as a new type of model with interesting implications. In the present paper the same limit is
Correlated Lattice Fermions in High Dimensions
A new approach to correlated Fermi systems such as the Hubbard model, the periodic Anderson model etc. is discussed, which makes use of the limit of high spatial dimensions. This limit — which is
Enhancement of the Magnetic Susceptibility of a Periodic Anderson Model
Magnetic susceptibility of a periodic Anderson model defined in infinite dimensions is investigated using the quantum Monte Carlo method. Special attention is paid to the enhancement of the interband
Linked-cluster expansion around the atomic limit of the Hubbard model.
  • Metzner
  • Physics, Medicine
    Physical review. B, Condensed matter
  • 1991
TLDR
Diagrammatic rules that determine the grand-canonical potential and the Green's functions are derived and reduce the calculation of any finite-order contribution to simple algebra, which opens the way for series extrapolations from computer-aided high-finite-order evaluations.
Gap Formation in the Symmetric Periodic Anderson Model in Infinite Dimensions
We study the symmetric periodic Anderson model in infinite dimensions by the selfconsistent second order perturbation theory. After solving the selfconsistent equations for the Green's functions, we
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition.
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