  We obtain the quantum phase diagram of the ionic Hubbard model including
electron-hole symmetric density-dependent hopping. The boundaries of the phases
are determined by crossing of excited levels with particular discrete
symmetries, which coincide with jumps of charge and spin Berry phases with a
topological meaning. Reducing the magnitude of the hopping terms that do not
change the total number of singly occupied sites with respect to the other one,
the region of the phase diagram occupied by the fully gapped spontaneously
dimerized insulator (which separates the band insulating and Mott insulating
phases) is enlarged, particularly for small values of the alternating on-site
energy. This result might be relevant for experiments in cold atoms in which
topological charge pumping is observed when alternation in the hopping is
included.
