Optical absorption of strongly correlated half-filled Mott-Hubbard chains

In this, the 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 compared with both the bandwidth W and the nearest-neighbour interaction V, the charge dynamics are 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-neighbour interaction V for the Neel 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 less than or equal to \omega - U\ less than or equal to W. The central peak at omega = U vanishes only for delta = 0 in the Neel state. For an appreciable nearest-neighbour 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 depend very sensitively on both the lattice and the spin dimerization of the ground state.