Spectral signatures of the Luttinger liquid to the charge-density-wave transition

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, the latter being either of the soft-mode or central-peak type. The generic features observed are relevant to several classes of low-dimensional materials.