Exact numerical methods for electron-phonon prob- lems

In the last few years solid state physics has increasingly benefited from scientific computing and the significance of numerical techniques is likely to keep on growing quickly in this field. Because of the high complexity of solids, which are made of a huge number of interacting electrons and nuclei, a full understanding of their properties cannot be developed using analytical methods only. Numerical simulations do not only provide quantitative results for the properties of specific materials but are also widely used to test the validity of theories and analytical approaches. Numerical and analytical approaches based on perturbation theory and effective independent-particle theories such as the Fermi liquid theory, the density functional theory, the Hartree-Fock approximation, or the Born-Oppenheimer approximation, have been extremely successful in explaining the properties of solids. However, the low-energy and low-temperature electronic, optical, or magnetic properties of various novel materials are not understood within these simplified theories. For example, in strongly