  We employ dynamical density-matrix renormalization group (DDMRG) and
field-theory methods to determine the frequency-dependent optical conductivity
in one-dimensional extended, half-filled Hubbard models. The field-theory
approach is applicable to the regime of `small' Mott gaps which is the most
difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers
analytical results obtained previously by means of strong-coupling techniques.
We focus on exciton formation at energies below the onset of the absorption
continuum. As a consequence of spin-charge separation, these Mott-Hubbard
excitons are bound states of spinless, charged excitations (`holon-antiholon'
pairs). We also determine exciton binding energies and sizes. In contrast to
simple band insulators, we observe that excitons exist in the Mott-insulating
phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore,
our results show that the exciton binding energy and size are not related in a
simple way to the strength of the Coulomb interaction.
