Density of states of a disordered Hubbard model using the modified moments method

Abstract

We apply the modified-moments method to compute the density of states of the impurity band of a doped semi-conductor in the intermediate region of impurity concentrations. This method is used to correct the density of states obtained by interpolating between the high and low concentration limit asymptotic expressions. The calculation is based on the Hubbard model in the atomic limit without spin ordering. The overlap integral is assumed to be a Gaussian function of the impurity separation. Use is made of the first seven moments of the exact distribution and of the low and high concentration limit approximations previously calculated. The first six moments are employed to determine the orthogonal polynomial expansion of the density of states while the seventh moment is used as a check on the accuracy of the distribution obtained. The results are similar to the previous ones using a truncated Edgeworth series for the correction term but the present method has the advantage of being a more systematic approach.