  Using the density matrix renormalization group algorithm, we investigate the
lattice model for spinless fermions in one dimension in the presence of a
strong interaction and disorder. The phase sensitivity of the ground state
energy is determined with high accuracy for systems up to a size of 60 lattice
constants. This quantity is found to be log-normally distributed. The
fluctuations grow algebraically with system size with a universal exponent of
~2/3 in the localized region of the phase diagram. Surprizingly, we find, for
an attractive interaction, a delocalized phase of finite extension. The
boundary of this delocalized phase is determined.
