Mobility edge of two interacting particles in three-dimensional random potentials
arXiv:1903.06214 · doi:10.1103/PhysRevB.99.224209
Abstract
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 non-monotonic 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.
accepted version with new discussion on density of states of effective model, references added
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- Absence of two-body delocalization transitions in the two-dimensional Anderson-Hubbard model
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