  Electron- and phonon spectral functions of the one-dimensional,
spinless-fermion Holstein model at half filling are calculated in the four
distinct regimes of the phase diagram, corresponding to an attractive or
repulsive Luttinger liquid at weak electron-phonon coupling, and a band- or
polaronic insulator at strong coupling. The results obtained by means of kernel
polynomial and systematic cluster approaches reveal substantially different
physics in these regimes and further indicate that the size of the phonon
frequency significantly affects the nature of the quantum Peierls phase
transition.
