  We study the zero-temperature phase diagram of the half-filled
one-dimensional ionic Hubbard model. This model is governed by the interplay of
the on-site Coulomb repulsion and an alternating one-particle potential.
Various many-body energy gaps, the charge-density-wave and bond-order
parameters, the electric as well as the bond-order susceptibilities, and the
density-density correlation function are calculated using the density-matrix
renormalization group method. In order to obtain a comprehensive picture, we
investigate systems with open as well as periodic boundary conditions and study
the physical properties in different sectors of the phase diagram. A careful
finite-size scaling analysis leads to results which give strong evidence in
favor of a scenario with two quantum critical points and an intermediate
spontaneously dimerized phase. Our results indicate that the phase transitions
are continuous. Using a scaling ansatz we are able to read off critical
exponents at the first critical point. In contrast to a bosonization approach,
we do not find Ising critical exponents. We show that the low-energy physics of
the strong coupling phase can only partly be understood in terms of the strong
coupling behavior of the ordinary Hubbard model.
