Generalizations of dynamical mean field theory by the lace expansion

We use the so-called lace expansion of mathematical random walk theory to d erive several generalizations of dynamical mean-field theory (DMFT) for str ongly correlated electron systems (SCES). DMFT is based on a self-consisten ce condition. by which a lattice Hamiltonian for SCES is mapped onto the co rresponding impurity problem. It is a local theory with a density of states of the impurity problem following from the local band Green function. So i n the Fourier-transformed version the self-energy is independent of momenta . From a mathematical point of view. the self-consistence condition follows from a physical self-avoiding loop. We discuss non-local as well as local corrections and examine them numerically for the Anderson lattice in the la rge U limit. All calculations are performed at finite spatial dimensions. ( C) 2001 Elsevier Science B.V. All rights reserved.