Application of the connected-moment expansion to single-impurity Anderson Hamiltonians.

The study of single-impurity Hamiltonians has, in recent years, been the focus of a great deal of attention. In particular, the Kondo model and the Anderson model have attracted a variety of calculational methods. These include pertubation theory, Hartree-Fock, mean field, renormalization-group theory, Bethe ansataz as well as a number of different variational schemes. Most recently Mancini, Potter, and Bowen' have applied a matrix truncation method that has shown a great deal of promise for estimating the ground-state energy of these systems. Here it was demonstrated that by choosing a truncated basis, with a small amount of effort rapid convergence is achieved and the exact results of the Bethe-ansatz calculations may be approached within a few percent. Recently, a novel calculational method, the connected-moment expansion (CME), was developed by Cioslowski and applied the various molecular Hamiltonians. This work was based on a theorem by Horn and Weinstein concerning the ground-state energy of manybody systems. For any trial ket ~ Po) the function F ( t ) = & go ~ exP( —tP )H ~ go ) I& fo~ exP( tH ) ~ lbo)— = g ( t)"It, +,lk!— k=0