2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/16131We propose a new optimized phonon approach for the numerical diagonalization of interacting electron-phonon systems combining density-matrix and Lanczos algorithms. We demonstrate the reliablity of this approach by calculating the phase diagram for bi-polaron formation in the one-dimensional Holstein-Hubbard model, and the Luttinger parameters for the metallic phase of the half-filled one-dimensional Holstein model of spinless fermions.4 pages, 4 figures included, submitted to Phys. Rev. BStrongly Correlated Electronstext