  Unconventional phases often occur where two competing mechanisms compensate.
An excellent example is the ionic Hubbard model where the alternating local
potential $\delta$, favoring a band insulator (BI), competes with the local
repulsion $U$, favoring a Mott insulator (MI). By continuous unitary
transformations we derive effective models in which we study the softening of
various excitons. The softening signals the instability towards new phases that
we describe on the mean-field level. On increasing $U$ from the BI in two
dimensions, we find a bond-ordered phase breaking orientational symmetry due to
a d-wave component. Then, antiferromagnetic order appears coexisting with the
d-wave bond order. Finally, the d-wave order vanishes and a N\'eel-type MI
persists.
