Wentzel-Bardeen singularity and phase diagram for interacting electrons coupled to acoustic phonons in one dimension

We consider strongly correlated electrons coupled to low-energy acoustic phonons in one dimension. Using a Luttinger liquid description we calculate the exponents of various response functions and discuss their remarkable sensitivity to the Wentzel-Bardeen singularity induced by the presence of phonons. For the Hubbard model plus phonons the equivalent of a phase diagram is established. By increasing the filling factor towards half filling the Wentzel-Bardeen singularity is approached. This in turn triggers a simple and efficient mechanism to suppress antiferromagnetic fluctuations and to drive the system via a normal metallic state towards a superconducting phase.