  In order to study the effect of interaction and lattice distortion on quantum
coherence in one-dimensional Fermi systems, we calculate the ground state
energy and the phase sensitivity of a ring of interacting spinless fermions on
a dimerized lattice. Our numerical DMRG (Density Matrix Renormalization Group)
studies, in which we keep up to 1000 states for systems of about 100 sites, are
supplemented by analytical considerations using bosonization techniques. We
find a delocalized phase for an attractive interaction, which differs from that
obtained for random lattice distortions. The extension of this delocalized
phase depends strongly on the dimerization induced modification of the
interaction. Taking into account the harmonic lattice energy, we find a
dimerized ground state for a repulsive interaction only. The dimerization is
suppressed at half filling, when the correlation gap becomes large.
