The excitation statistics of disordered strongly correlated systems

The level statistics of a tight-binding Hamiltonian describing strongly interacting particles in a disordered system is investigated. It is found to be characterized by two transitions as functions of interaction strength. The first is from Poisson statistics to Wigner (GOE) statistics as interactions between the particles are turned on, and the second is back to Poisson statistics as the interactions become stronger. The dependences of both transitions on the interaction strength, filling factor, size of the sample, disorder and range of interactions are considered. Possible experimental consequences are discussed.