Strong correlations and electron-phonon coupling in high-temperature superconductors: a quantum Monte Carlo study

We present quantum simulation studies for a system of strongly correlated fermions coupled to local anharmonic phonons. The Monte Carlo calculations are based on a generalized version of the Projector Quantum Monte Carlo Method allowing a simultaneous treatment of fermions and dynamical phonons. The numerical simulations yield exact results in the electron-phonon parameter regime relevant for high-$T_{\rm c}$ superconductivity, which is not accessible by perturbative methods like Eliashberg-Theory. The class of electron-phonon-models covered in the simulations describes superconductivity exhibiting several features of the new high-$T_{\rm c}$ materials