ELECTRON-PHONON COUPLING CLOSE TO A METAL-INSULATOR-TRANSITION IN ONE-DIMENSION

We consider a one-dimensional system of electrons interacting via a sh ort-range repulsion and coupled to phonons close to the metal-insulato r transition at half-filling. We argue that the metal-insulator transi tion can be described as a standard one-dimensional incommensurate to commensurate transition, even if the electronic system is coupled to t he lattice distortion. By making use of known results for this transit ion, we prove that low-momentum phonons, with the inclusion of the 4k( F) (similar or equal to 2 pi near half-filling) scattering, do not pla y any relevant role close to the metal-insulator transition, unless th eir coupling to the electrons is large in comparison with the other en ergy scales present in the problem. In other words the effective stren gth of the low-momentum transferred electron-phonon coupling does not increase close to the metal-insulator transition, even though the effe ctive velocity of the mobile carriers is strongly diminished.