Optische Anregungen in eindimensionalen Peierls-Hubbard-Modellen

In this work the optical excitations in the one-dimensional extended Peierls-Hubbard model are studied. There are two competing interactions in this model, namely the Coulomb interaction and the Peierls interaction. The latter causes a dimerised lattice structure. To calculate the optical excitations perturbatively, one needs to identify the dominant interaction of the model. In the field-theoretical limit using different methods, such as a semiclassical approach, mean-field theory and the renormalisation group, one finds that it is the Peierls-interaction which dominates the system and therefore defines the starting point for perturbation theory. Rayleigh-Schrödinger perturbation theory is carried out up to second order in the weak Coulomb interaction for the ground-state energy and the one-particle gap. The singlet and triplet exciton gaps, i.e. charge and spin gap, are calculated using Wannier perturbation theory, two-step perturbation theory and Downfolding perturbation theory. All results are compared to results obtained by using the density-matrix renormalisation group approach (DMRG).