On a Generalized-Moments Method

Abstract

The continued-fraction technique has been widely used in solid state physics. It provides a useful theoretical framework for calculating the densities of states (of electrons, phonons...) mainly in disordered systems. The continued-fraction coefficients are computed either from the moments of the density of states or more directly by the recursion method. The former has the advantage of the linearity upon the density of states and the latter is numerically optimized. The generalized-moments method is an interpolation between both methods that, if suitably used, combines their advantages. A version of the method could be seen as a perturbation expansion from the Bethe lattice. The asymptotic limits of the continued-fraction coefficients are shown to be accurately determined from the generalized-moments associated to the recursion method. Computations of electronic densities of states illustrate the method.