  Single-- and two-particle excitation spectra of the one-dimensional,
half-filled Holstein-Hubbard model are calculated using the continuous-time
quantum Monte Carlo method. In the metallic phase, the results are consistent
with a Luther-Emery liquid that has gapped spin and single-particle excitations
but a gapless charge mode. However, given the initially exponential dependence
of the spin gap on the backscattering matrix element, the numerical excitation
spectra appear gapless in the weak-coupling regime, and therefore resemble
those of a Luttinger liquid. The Mott phase has the expected charge gap and
gapless spin excitations. The Peierls state shows a charge, spin and
single-particle gap, a soft phonon mode, backfolded shadow bands and soliton
excitations. Arguments and numerical evidence for the existence of a nonzero
spin gap throughout the metallic phase are provided in terms of equal-time spin
and charge correlation functions.
