Coulomb repulsion versus Hubbard repulsion in a disordered chain

We study the difference between on site Hubbard and long range Coulomb repulsions for two interacting particles in a disordered chain. While Hubbard repulsion can only yield weak critical chaos with intermediate spectral statistics, Coulomb repulsion can drive the two particle system to quantum chaos with Wigner-Dyson spectral statistics. For intermediate strengths U of the two repulsions in one dimension, there is a crossover regime where delocalization and spectral rigidity are maximum, whereas the limits of weak and strong U are characterized by a stronger localization and uncorrelated energy levels.