Optimized phonon approach for the diagonalization of electron-phonon problems

We 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.