Optical absorption of strongly correlated half-filled Mott-Hubbard   chains
  In this last of three articles on the optical absorption of electrons in a half-filled Peierls-distorted chain we address the dimerized extended Hubbard model in the limit of a large on-site interaction $U$. When the Hubbard interaction is large both compared to the band width $W$ and the nearest neighbor interaction $V$ the charge dynamics is properly described by the Harris-Lange model. This model can be exactly mapped onto a model of free spinless Fermions in parallel (Hubbard-)bands of width $W$ which are eventually Peierls-split. To determine the coherent absorption features at low temperatures we design and employ the ``no-recoil approximation'' in which we assume that the momentum transfer to the spin degrees of freedom can only be $\Delta q_S=0$ or $\Delta q_S=\pi/a$ during an optical excitation. We present explicit analytical results for the optical absorption in the presence of a lattice dimerization $\delta$ and a nearest-neighbor interaction $V$ for the N\'{e}el and dimer state. We find that the coherent part of the optical absorption for $V=0$ is given by a single peak at $\omega=U$ and broad but weak absorption bands for $W\delta\leq |\omega-U| \leq W$. The central peak at $\omega=U$ only vanishes for $\delta=0$ in the N\'{e}el state. For an appreciable nearest neighbor interaction $V>W/2$ almost all spectral weight is transferred to the $\Delta q_C=0$-exciton and the $\Delta q_C=\pi/a$-exciton whose relative spectral weights very sensitively depend on both the lattice and the spin dimerization of the ground state. 
F. Gebhard (ILL Grenoble, France), K. Bott, M. Scheidler, P. Thomas,   and S. W. Koch (Philipps University Marburg, Germany)