Sparse random matrix configurations for two or three interacting electrons in a random potential
arXiv:cond-mat/9703188 · doi:10.1103/PhysRevB.56.13623
Abstract
We investigate the random matrix configurations for two or three interacting electrons in one-dimensional disordered systems. In a suitable non-interacting localized electron basis we obtain a sparse random matrix with very long tails which is different from a superimposed random band matrix usually thought to be valid. The number of non-zero off-diagonal matrix elements is shown to decay very weakly from the matrix diagonal and the non-zero matrix elements are distributed according to a Lorentzian around zero with also very weakly decaying parameters. The corresponding random matrix for three interacting electrons is similar but even more sparse.
10 pages, Latex file, 5 postscript files