Non-Fermi liquid over an extended range at zero temperature in the Holstein model away from half-filling

We investigate the evolution of the normal state in the electron-phonon coupled Holstein model away from half-filling in infinite dimensions. Using dynamical mean-field theory in conjunction with Wilson's numerical renormalization group (NRG), we construct the zero-temperature phase diagram, identifying three distinct phases: Fermi liquid metal (FLM), spin-gap metal (SGM), and spin-gap insulator (SGI). A first-order transition is observed between the FLM and SGM phases, driven by spin-gap pairing in the absence of a charge gap, while a metal-insulator transition between SGM and SGI occurs through regions of phase coexistence. Furthermore, we demonstrate that the SGM phase of the Holstein model away from half-filling, characterized by the NRG valence-fluctuation fixed point, serves as a prototype for non-Fermi liquid (NFL) metallic behavior arising from onsite pairing. Notably, near the FLM-NFL phase boundary, strong lattice fluctuations emerge, which are expected to enhance superconductivity.