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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 $Δq_S=0$ or $Δq_S=π/a$ during an optical excitation. We present explicit analytical results for the optical absorption in the presence of a lattice dimerization $δ$ and a nearest-neighbor interaction $V$ for the Néel and dimer state. We find that the coherent part of the optical absorption for $V=0$ is given by a single peak at $ω=U$ and broad but weak absorption bands for $Wδ\leq |ω-U| \leq W$. The central peak at $ω=U$ only vanishes for $δ=0$ in the Néel state. For an appreciable nearest neighbor interaction $V>W/2$ almost all spectral weight is transferred to the $Δq_C=0$-exciton and the $Δq_C=π/a$-exciton whose relative spectral weights very sensitively depend on both the lattice and the spin dimerization of the ground state.