  We investigate the ground-state phase diagram of the Hubbard model for the
AB$_{N-1}$ chain with filling 1/N, where $N$ is the number of atoms per unit
cell. In the strong-coupling limit, a charge transition takes place from a band
insulator (BI) to a correlated insulator (CI) for increasing on-site repulsion
$U$ and positive on-site energy difference $\Delta$ (energy at A sites lower
than at B sites). In the weak-coupling limit, a bosonization analysis suggests
that for $N > 2$ the physics is qualitatively similar to the case $N = 2$ which
has already been studied: an intermediate phase emerges, which corresponds to a
bond-ordered ferroelectric insulator (FI) with spontaneously broken inversion
symmetry. We have determined the quantum phase diagram for the cases $N = 3$
and $N = 4$ from the crossings of energy levels of appropriate excited states,
which correspond to jumps in the charge and spin Berry phases, and from the
change of sign of the localization parameter $z_{L}^{c}$. From these techniques
we find that, quantitatively, the BI and FI phases are broader for $N > 2$ than
when $N = 2$, in agreement with the bosonization analysis. Calculations of the
Drude weight and $z_{L}^{c}$ indicate that the system is insulating for all
parameters, with the possible exception of the boundary between the BI and FI
phases.
