  To investigate the influence of electronic interaction on the metal-insulator
transition (MIT), we consider the Aubry-Andr\'{e} (or Harper) model which
describes a quasiperiodic one-dimensional quantum system of non-interacting
electrons and exhibits an MIT. For a two-particle system, we study the effect
of a Hubbard interaction on the transition by means of the transfer-matrix
method and finite-size scaling. In agreement with previous studies we find that
the interaction localizes some states in the otherwise metallic phase of the
system. Nevertheless, the MIT remains unaffected by the interaction. For a
long-range interaction, many more states become localized for sufficiently
large interaction strength and the MIT appears to shift towards smaller
quasiperiodic potential strength.
