Sparse-random-matrix configurations for two or three interacting electrons in a random potential

We investigate the random-matrix configurations for two or three interacting electrons in one-dimensional disordered systems. In a suitable noninteracting localized electron basis we obtain a sparse random matrix with very long tails which is different from the superimposed random-band-matrix description usually thought to be valid. The number of nonzero off-diagonal matrix elements decays very weakly from the matrix diagonal and their distribution is a Lorentzian having long tails. The corresponding random matrix for three interacting electrons is similar but even more sparse.