The radius of convergence of dynamical mean-field theory

The dynamical mean-field theory (DMFT) maps the periodic Anderson-model for infinite U onto a single impurity model with an effective band. This effective band is approximately described by a self-avoiding loop through the lattice with a local scattering matrix and can be written as a power series in that matrix times the unperturbed nearest neighbor propagator. We show that the power series has a finite radius of convergence, which is given by the inverse of the connective constant. In the limit of infinite spatial dimensions, in which the DMFT becomes exact, the underlying self-avoiding loop has zero radius of convergence. We also further comment on the breakdown of one self-consistency condition in the DMFT. (C) 2002 Elsevier Science B.V. All rights reserved.