Competing and cooperative effects of spin, charge, and phonon degrees of freedom in HTSC

The phase diagram of high-T-c superconducting copper oxides (HTSC) exhibits an unusual complexity which is, at present, beyond any microscopic modeling. Motivated by very recent experimental findings-(i) a giant isotope effect on T* and (ii) doping-dependent phonon anomalies and "extra" modes-the role played by the lattice is reinvestigated and the consequences arising for the striped phase are discussed. By including nonlinear higher-order phonon-phonon and density-density interactions in the Hamiltonian, an isotope effect on T* is obtained, as well as substantial q-dependent phonon anomalies, where both effects are strongly doping dependent.