  We analyze the global ground-state (quantum) phase diagram of the
one-dimensional Holstein model at half-filling as a function of the strength of
the electron-phonon coupling (represented by the strength of the phonon-induced
attraction, $U$) and the phonon frequency, $\omega_0$. In addition to
reanalyzing the various asymptotic regimes, we have carried out density-matrix
renormalization group simulations to correct previous inferences concerning the
anti-adiabatic (large $\omega_0$) and strong coupling (large $U$) regimes.
There are two distinct phases - a fully gapped commensurate charge-density-wave
and a spin-gapped Luther-Emery phase with a gapless charge mode - separated by
a phase boundary, with a shape that reflects different microscopic physics in
the weak and strong coupling limits.
