Effective use of the recursion method in the study of disordered systems

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Abstract
A self-consistent approach to the study of disordered systems with the use of the recursion method is examined in detail using the diamond lattice as the basic structure. In this method the average local Green's function depends upon two parameters: the number of particles (shell size) and the number of configurations. We apply this approach to calculate the electronic density of states in the Anderson model and the vibrational spectrum of an isotopically disordered diamond lattice. We find that there is no need to go beyond the eleventh shell to obtain a realistic description of the system even for cases which are primarily extended states and that a detailed accounting of the fine structure associated with localized states may require about 1000 configurations in the ensemble-averaging process. The computation times are well within reach in even the most extreme cases.