Mobility edge of two interacting particles in three-dimensional random potentials

We investigate Anderson transitions for a system of two particles moving in a three-dimensional disordered lattice and subject to on-site (Hubbard) interactions of strength U. The two-body problem is exactly mapped into an effective single-particle equation for the center-of-mass motion, whose localization properties are studied numerically. We show that, for zero total energy of the pair, the transition occurs in a regime where all single-particle states are localized. In particular, the critical disorder strength exhibits a nonmonotonic behavior as a function of |U|, increasing sharply for weak interactions and converging to a finite value in the strong-coupling limit. Within our numerical accuracy, short-range interactions do not affect the universality class of the transition.