Polarons in Correlated Materials

Modern materials offer a variety of highly interesting properties like, e.g., high-temperature superconductivity, colossal magneto-resistance or large thermo power. In many cases, the materials and their properties can only be understood, if one takes into account the interaction between their electrons and between the electrons and lattice fluctuations, i.e., phonons. In order to gain insights about the mechanisms at work, one tries to capture the most important aspects into simplified models. Solving these models is still very difficult, and one usually tries numerical simulation or analytical approximations. While numerical methods may not need approximations, they are limited by the available computational power: In many cases, the needed resources grow exponentially fast with the system size, so that only very small clusters or approximations to the real situation can be investigated. Analytical solutions are not only faster to evaluate, but can also often lead to additional insights into the relevant physics. Analytical approaches usually need more or less severe approximation, which restricts their validity. Recently, however, a new approximation has been developed for the Holstein polaron formed by an electron interacting with phonons. This `Momentum Average Approach` has been found to describe the highly non-trivial many-body problem with high accuracy in all parameter regimes. The approach is also rather flexible, and we propose to generalize it to a hole interacting with phonons as well as with the magnetic and orbital degrees of freedom, i.e., magnons or orbitons. This situation is of fundamental interest in strongly correlated systems, and has been treated by a variety of numerical and analytical approaches involving various approximations. We will will use the numerical Cluster Perturbation Theory for the same situation and will thus be able to compare analytical and numerical results. We further propose to generalize the Momentum Average Approach to two-particle Green`s functions for the two- electron (or hole) case. The two-particle case is important because it gives indications about the interaction between individual polarons, and two-particle Green`s functions like the optical conductivity can be related to experimentally observed quantitates.