Fictive impurity models: An alternative formulation of the cluster dynamical mean-field method

(Dated: February 2, 2008)‘Cluster’ extensions of the dynamical mean field method to include longer range correlations arediscussed. It is argued that the clusters arising in these methods are naturally interpreted not asactual subunits of a physical lattice but as algorithms for computing coefficients in an orthogonalfunction expansion of the momentum dependence of the electronic self-energy. The difficulties withcausality which have been found to plague cluster dynamical mean field methods are shown to berelated to the ‘ringing’ phenomenon familiar from Fourier analysis. The analogy is used to motivateproposals for simple filtering methods to circumvent them. The formalism is tested by comparisonto low order perturbative calculations and self consistent solutions.I. INTRODUCTION