  The effects of quantum lattice fluctuations on the Peierls transition are
studied within the one--dimensional Holstein molecular crystal model by means
of exact diagonalization methods. Applying a very efficient variational Lanczos
technique, the ground--state phase diagram is obtained in excellent agreement
with predictions of recent density matrix renormalization group calculations.
The transition to the charge--density--wave regime is signaled by a strong
increase in the charge structure factor. In the metallic regime, the
non--universal Luttinger liquid parameters (charge velocity and coupling
constant) are deduced from a finite--size scaling analysis. The variational
results are supported by a complete numerical solution of the quantum phonon
Holstein model on small clusters, which is based on a well--controlled phonon
Hilbert space truncation procedure. The metallic and charge--density--wave
phases are characterized by significant differences in the calculated optical
absorption spectra.

Strongly Correlated Electrons