New Iterative Perturbation Scheme for Lattice Models with Arbitrary Filling.

In recent years there has been a renewed interest in the study of strongly correlated electron materials. These materials exhibit interesting phenomena like the correlation induced metal insulator transition [1–3]. A very promising method capable of providing a theoretical description, perhaps, is the limit of large spatial dimensions [4], which defines a dynamical mean field theory for the problem. This limit can be mapped onto an impurity model together with a self-consistency condition which is characteristic for the specific model under consideration [5]. The mapping allows one to apply several numerical and analytical techniques which have been developed to analyze impurity models over the years. There are different approaches which have been used for this purpose: qualitative analysis of the mean field equations [5], quantum Monte Carlo methods [6–8], iterative perturbation theory (IPT) [5,9], exact diagonalization methods [10,11], and the projective self-consistent method, a renormalization technique [12]. However, each of these methods has its shortfalls. While quantum Monte Carlo calculations are not applicable in the zero temperature limit, the exact diagonalization methods and the projective self-consistent method yield only a discrete number of poles for the density of states. Moreover, the computational requirements of the exact diagonalization and the quantum Monte Carlo methods are such that they can only be implemented for the simplest Hamiltonians. To carry out realistic calculations it is necessary to have an accurate but fast algorithm for solving the impurity model. In this context iterative perturbation theory has turned out to be a useful and reliable tool for the case of half filling [13,14]. However, for finite doping the naive extension of the IPT scheme is known to give unphysical results. There is still no method which can be applied away from half filling and which at the same time is powerful enough to treat more complicated models. The aim of this paper is to close this gap by introducing a new iterative perturbation scheme which is applicable at arbitrary filling. The (asymmetric) Anderson impurity model