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, $ω_0$. 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 $ω_0$) 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.

14 pages, 13 figures