Effect of phonon dispersion on the competition between pairing and charge order

The Holstein Model (HM) describes the interaction between fermions and a collection of local
(dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions,
giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective
superconducting (SC) and charge density wave (CDW) phases. Quantum Monte Carlo (QMC)
simulations have considered both these limits, but have not yet focused on the physics of more
general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and
CDW order in such models. We quantify the effect of finite phonon bandwidth and curvature on the
critical temperature T_cdw for CDW order, and also uncover several novel features of diagonal long
range order in the phase diagram, including a competition between charge patterns at momenta
q =(π,π) and q=(π, 0), which lends insight into the relationship between Fermi surface nesting
and the wavevector at which charge order occurs. We also demonstrate off-diagonal (SC) order at
half-lling in situations where nonzero bandwidth suffciently suppresses T_cdw.