We analyze the dynamic scattering amplitude between quasiparticles at the Fermi surface in the proximity of a charge instability, which may occur in the high temperature superconductors. Within the infinite-$U$ Hubbard-Holstein model we find that in the absence of long-range Coulomb forces the scattering amplitude is strongly singular at zero momentum transfer close to the phase separation instability. In the presence of long-range Coulomb forces the singularity occurs at finite wave vectors. In both cases we show how normal state properties are largely affected by this scattering.

Pervasive fluctuations: Among the many intertwined phases in the cuprate superconductor phase diagram is the charge density wave (CDW) order, which has been detected in all major cuprate families. It is thought that CDW competes with superconductivity, but whether it has bearing on the mechanism of superconductivity remains unclear. Arpaia et al. undertook a comprehensive study of charge density fluctuations in a cuprate family, varying doping and temperature. They found that short-range dynamic charge fluctuations were present in a large portion of the phase diagram, at temperatures considerably higher than those at which the CDW order disappears. Science , this issue p. 906

The conditions leading to small-polaron formation for a single charge carrier in the Su-Schrieffer-Heeger (SSH) model are compared with the Holstein model. From analytic perturbation theory and exact numerical diagonalization of small clusters different criteria are established, which however have a common physical origin: Polaron formation requires a sizable mass enhancement and a lattice deformation energy gain larger than the loss in the bare electron kinetic energy in both models. The optical absorption of the Su-Schrieffer-Heeger model in the polaronic regime is also shown to exhibit an additional feature not present in the Holstein model. This additional feature arises due to the bond nature of small polarons in the SSH model, and is determined by transitions from the ground state of the bonding character on a shortened bond to excited states of the antibonding character on the same shortened bond.