CONSTRUCTION OF SIZE-CONSISTENT EFFECTIVE-HAMILTONIANS

For a system consisting of two interacting subsystems, effective Hamil tonians for one subsystem are usually constructed by integrating out t he degrees of freedom of the second subsystem. In contrast to usual tr eatments, our method for deriving effective Hamiltonians is based on t he introduction of cumulants. Cumulants guarantee size consistency, a property that is not always evident in other approaches. The formalism applies for any temperature. Our method is based on a matrix formulat ion in the framework of a recently introduced cumulant-projection meth od. This method allows the treatment of strongly correlated systems, w here conventional diagrammatic techniques are difficult to apply. The relation with perturbation theory is also shown. As a simple applicati on we discuss the small polaron problem. Evaluating the one-electron d ispersion relation in the strong-coupling case shows good agreement wi th recent results from exact Lanczos diagonalization. Our method has s ubstantial advantages over perturbation theory.