Kinks and waterfalls in the dispersion of ARPES features

In this paper we use a generic form for the Green function G(k, ω) in a correlated metal, already proven successful in describing ARPES line shapes [1]. The associated many body self-energy function has only a single pole. We now investigate, whether this generic model can be used all the way to the limit of strong correlations and, when applied to ARPES intensities, whether it is able to explain some of the ubiquitous dispersive crossover phenomena that have been attributed to dynamical, i.e.: ω-dependent effects. We argue that a quantitative interpretation of experimental data requires to calculate extrema not only in the momentum distribution curve but also in the energy distribution curve. In passing, we give a formula for the extrema in the latter distribution that is valid for the general G(k, ω) in a many body system. To our knowledge, this is a new formula, not found in the literature. The investigation of the generic model proceeds on two levels: on the one hand, we explore the rich variety of crossovers that can be predicted and linked to well defined features in the complex ω-plain. On the other hand, we show that the generic one-pole self-energy can be viewed as a projection on the low energy sector of a microscopic solution, belonging to a lattice model of interacting fermions. To obtain approximate microscopic solutions, we use our continued fraction method [2,3]. As an explicit example, we study the projection for the case of a hole doped Hubbard model in infinite dimension. A discussion section gives examples, how the generic model is able to cope with the ubiquity of the crossover phenomena, also in finite dimension and beyond the Hubbard model.