Renormalization group study of the electron-phonon interaction in high-Tc cuprates

We generalize the numerical renormalization group (RG) scheme of Honerkamp et al. (Phys. Rev. B, 63 (2001) 035109), Zanchi et al. (Europhys. Lett., 44 (1997) 235; Phys. Rev. B, 61 (2000) 13609) and Halboth et al. (Phys. Rev. Lett., 85 (2000) 5162) to study the phonon-mediated retarded interactions in the high-T-c cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a x(2)-y(2) symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around (pi/a, pi/a). After growing strong, these retarded interaction will trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders.