Superconductivity and charge density wave order in the doped Holstein model

The Holstein model (HM) is a tight-binding Hamiltonian which describes the interaction between electrons and local phonon modes on a lattice. Although charge density wave (CDW) order dominates at half-filling, the electron-phonon interaction is known to give rise to superconducting (SC) order away from half-filling. We use Determinant Quantum Monte Carlo (DQMC) simulations to explore the onset of SC order in doped systems through measurements of the s-wave pair susceptibility. We provide estimates for the critical temperature of the SC transition, obtained through a scaling analysis, for various values of the electron-phonon coupling λ and phonon frequency ω. We also explore the possible existence of an incommensurate CDW phase away from half-filling through measurements of the CDW structure factor.