  The ground state energies of infinite half-filled Hubbard-Peierls chains are
investigated combining incremental expansion with exact diagonalization of
finite chain segments. The ground state energy of equidistant infinite Hubbard
(Heisenberg) chains is calculated with a relative error of less than $3 \cdot
10^{-3}$ for all values of $U$ using diagonalizations of 12-site (20-site)
chain segm ents. For dimerized chains the dimerization order parameter $d$ as a
function of the onsite repulsion interaction $U$ has a maximum at nonzero
values of $U$, if the electron-phonon coupling $g$ is lower than a critical
value $g_c$. The critical value $g_c$ is found with high accuracy to be
$g_c=0.69$. For smaller values of $g$ the position of the maximum of $d(U)$ is
approximately $3t$, and rapidly tends to zero as $g$ approaches $g_c$ from
below. We show how our method can be applied to calculate breathers for the
problem of phonon dynamics in Hubbard-Peierls systems.
