  We study the spectrum and eigenstates of the quantum discrete Bose-Hubbard
Hamiltonian in a finite one-dimensional lattice containing two bosons. The
interaction between the bosons leads to an algebraic localization of the
modified extended states in the normal mode space of the noninteracting system.
Weight functions of the eigenstates in the space of normal modes are computed
by using numerical diagonalization and perturbation theory. We find that
staggered states do not compactify in the dilute limit for large chains.
