Anderson localization versus delocalization of interacting fermions in one dimension

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 approximate to 2/3 in the localized region of he phase diagram. Surprisingly we find, for an attractive interaction, a delocalized phase of finite extension. The boundary of this delocalized phase is determined.