Correlated fermions on a lattice in high dimensions

Abstract

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 applied to a family of lattice fermion models with generalized kinetic and potential energies. A simple method is introduced for investigating the important issue of handling momentum conservation at the interaction vertices. It is shown that the irrelevance of momentum conservation found by Metzner and Vollhardt applies more generally than their Gaussian density of states. Interactions between particles on different sites are shown to simplify to their Hartree substitute. This leaves on-site interactions as the only dynamical interactions in the limit of infinite dimension.