Critical Spectral Statistics at the Metal-Insulator Transition in Interacting Fermionic Systems

The spectral properties of a disordered system with few interacting three-dimensional spinless fermions are investigated. We show the existence of a critical spacings distribution which is invariant upon increase of the system size, but strongly depends on the number of particles. At the critical point, we report a substantial decrease of the degree of level repulsion as the number of particles increases indicating a decrease of nearest level correlations associated with the sparsity of the Hamiltonian matrix.