Time-Dependent Many-Body Perturbation Theory: Possibilities and Limitations

This dissertation investigates the possibilities and limitations of time-dependent many-body perturbation theory by studying small Hubbard clusters for which the exact solution is available. The first part of the thesis is comprised of a short introduction to the concepts and methodologies used. The second part consists of an review of the main findings of the thesis and a short summary of four original papers. In paper I we study the dynamics of short Hubbard chains within many-body perturbation theory and compare to the exact solution. The main outcomes are that the T-matrix approximation works well in the low filling regime and that all approximation which involve correlation effects develop an unphysical steady state. In paper II we present the methodology used in paper I. We find that the correlation-induced damping appears even in the presence of leads and that there are multiple steady and quasi steady states. In paper III we make a review of the status of time dependent density functional theory for lattice models. In particular we find that a non-perturbative adiabatic local density approximation describes strong correlations well while many-body perturbation theory accounts better for non-adiabatic effects. In paper IV we propose a method to obtain the double occupancy from the Kadanoff-Baym equations. We show that the positiveness condition may be violated in the GW or the second Born approximation but fulfiled in the T-matrix approximation. We apply this method to obtain the local entanglement entropy