Approximate Methods

Abstract

Despite its conceptional simplicity the Hubbard model provides a complicated interacting many-electron problem which, in general, cannot be solved exactly. Therefore, approximate methods are employed which are presumed to give a qualitatively correct picture of the physics contained in the model. Here we are interested in the metal---insulator transition and other phenomena beyond perturbation theory. Hence, we have to design feasible non-perturbative approaches that also allow for the description of possible phase transitions.