Hubbard model in high dimensions: A perturbation expansion about the atomic limit

Walter Metzner

We develop a perturbation expansion in the intersite hopping around the atomic limit of the Hubbard model. It is valid for arbitrary finite temperatures and interaction strengths. Diagrammatic rules that determine the grand-canonical potential and the Green's functions are derived. They reduce the calculation of any finite-order contribution to simple algebra. This opens the way for series extrapolations from computer-aided high-finite-order evaluations. Discrepancies in earlier expansions around the atomic limit are clarified. The present expansion scheme involves only connected diagrams with unrestricted lattice sums. This allows one to perform a vertex renormalization as for the linked-cluster expansion of the Ising model. The renormalized perturbation expansion can be used to construct self-consistent approximations which are automatically exact in the atomic limit. In the limit of high lattice dimensions, only fully two-particle reducible embeddings of diagrams on the lattice contribute. The single-particle properties of the infinite-dimensional Hubbard model reduce to those of independent tight-binding fermions hopping between dressed sites.

S. Pairault, David Sénéchal, A.–M. S. Tremblay

Li Liu, Hong Yao, Steven Allan Kivelson

L. Craco, M. A. Gusmão

We discuss the infinite dimension limit of the Hubbard model by means of a perturbative expansion of the one-particle Green's function around the atomic limit. The diagrammatic structure is simplified in this limit, allowing a formal resummation that reproduces a previously proposed mapping to a single-site mean-field problem. The method provides a natural way of addressing this effective problem by means of a perturbative expansion in the local mean field. This gives the correct exact result for the Falicov-Kimball model, which is used as a starting point to study the Hubbard case. \textcopyright{} 1996 The American Physical Society.

Florian Gebhard

Colin J. Thompson, Sam Y. S. Yang, Anthony John Guttmann +1 more

High-temperature expansions for the strongly correlated Hubbard model in the limit of infinite spatial dimension d, with hopping scaled by d -1 2/, are developed for the Gibbs free energy and susceptibility to order T -10 for arbitrary values of the density. From Pade and other analysis the authors find no evidence of a phase transition at a finite critical temperature for any value of the density.