Thouless numbers for few-particle systems with disorder and interactions

Considering N spinless Fermions in a random potential, the delocalization of N-body states due to a short-range pairwise interaction is investigated in the basis of the one-particle Slater determinants, and the spectral rigidity of the N-body spectrum. The maximum number gN of consecutive levels exhibiting the universal Wigner-Dyson rigidity, the Thouless number, is given as a function of the strength U of the interaction for the bulk of the spectrum. A self consistent argument gives this relation to be gN∝UN/(N-1). The predictions are compared to a numerical study of three spinless Fermions in a disordered cubic lattice. Implications for the interaction-induced N-particle delocalization in real space are discussed.