Recent quantum Monte Carlo Dynamical Cluster calculations show that the Hubbard model displays superconductivity at temperatures relevant to the cuprate high temperature superconductors  suggesting that spin fluctuations may be responsible for superconductivity in these materials . Nevertheless, recent experiments (ARPES, isotope effect,…) show evidence of very strong electron-phonon interactions. We study the role of buckling, breathing and local phonon modes in the doped Hubbard model. We find that the synergistic interplay of antiferromagnetic correlations and the electron-phonon interaction strongly enhances polaron formation, antiferromagnetism, and the strength of the spin-mediated pairing interaction. Despite the latter effect, the buckling and breathing phonons suppress the superconductivity in the region of parameter space relevant for cuprate superconductors, while the pairing interaction remains electronic in origin. This is due to strong polaron formation and the subsequent suppression of the quasiparticle fraction. The low energy single-particle spectra and isotope effect are in agreement with experment.
 Systematic Study of d-Wave Superconductivity in the 2D Repulsive Hubbard Model T. A. Maier, M. Jarrell, T. C. Schulthess, P. R. C. Kent, and J. B. White Phys. Rev. Lett. 95, 237001 (2005)
 Structure of the Pairing Interaction in the Two-Dimensional Hubbard Model T. A. Maier, M. S. Jarrell, and D. J. Scalapino Phys. Rev. Lett. 96, 047005 (2006)
 Synergistic Polaron Formation in the Hubbard-Holstein Model at Small Doping, Alexandru Macridin, Brian Moritz, M. Jarrell and Thomas Maier, accepted Phys. Rev. Lett. (cond-mat/0607623)
 Suppression of superconductivity in the Hubbard model by buckling and breathing phonons, Alexandru Macridin, Brian Moritz, M. Jarrell and Thomas Maier, preprint, submitted to Phys. Rev. Lett. .