The density-matrix renormalization group (DMRG) is employed to calculate optical properties of the half-filled Hubbard model with nearest-neighbor interactions. In order to model the optical excitations of oligoenes, a Peierls dimerization is included whose strength for the single bonds may fluctuate. Systems with up to 100 electrons are investigated, their wave functions are analyzed, and relevant length-scales for the low-lying optical excitations are identified. The presented approach provides a concise picture for the size dependence of the optical absorption in oligoenes.
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