  We investigate the ground state phase diagram of the half-filled
$t-t^{\prime}$ repulsive Hubbard model in the presence of a staggered ionic
potential $\Delta$, using the continuum-limit bosonization approach. We find,
that with increasing on-site-repulsion $U$, depending on the value of the
next-nearest-hopping amplitude $t^{\prime}$, the model shows three different
versions of the ground state phase diagram. For $t^{\prime} <
t^{\prime}_{\ast}$, the ground state phase diagram consists of the following
three insulating phases: Band-Insulator at $U<U_{c}$, Ferroelectric Insulator
at $U_{c} < U < U_{s}$ and correlated (Mott) Insulator at $U > U_{c}$. For
$t^{\prime} > t^{\prime}_{c}$ there is only one transition from a spin gapped
metallic phase at $U<U_{c}$ to a ferroelectric insulator at $U > U_{c}$.
Finally, for intermediate values of the next-nearest-hopping amplitude
$t^{\prime}_{\ast} < t^{\prime} < t^{\prime}_{c}$ we find that with increasing
on-site repulsion, at $U_{c1}$ the model undergoes a second-order
commensurate-incommensurate type transition from a band insulator into a
metallic state and at larger $U_{c2}$ there is a Kosterlitz-Thouless type
transition from a metal into a ferroelectric insulator.
