2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100544We study the one-dimensional Holstein model of spinless fermions interacting with dispersion-less phonons by using a recently developed projector-based renormalization method (PRM). At half-filling the system shows a metal-insulator transition to a Peierls distorted state at a critical electron-phonon coupling where both phases are described within the same theoretical framework. The transition is accompanied by a phonon softening at the Brillouin zone boundary and a gap in the electronic spectrum. For different filling, the phonon softening appears away from the Brillouin zone boundary and thus reflects a different type of broken symmetry state.8 pages, 4 figures included; v2: completely revised and extended; v3: minor changes, final version, to be published in Eur. Phys. J. BStrongly Correlated Electronstext