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

摘要

In this last of three articles on the optical absorption of electrons in ahalf-filled Peierls-distorted chain we address the dimerized extended Hubbardmodel in the limit of a large on-site interaction $U$. When the Hubbardinteraction is large both compared to the band width $W$ and the nearestneighbor interaction $V$ the charge dynamics is properly described by theHarris-Lange model. This model can be exactly mapped onto a model of freespinless Fermions in parallel (Hubbard-)bands of width $W$ which are eventuallyPeierls-split. To determine the coherent absorption features at lowtemperatures we design and employ the ``no-recoil approximation'' in which weassume 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 presentexplicit analytical results for the optical absorption in the presence of alattice dimerization $\delta$ and a nearest-neighbor interaction $V$ for theN\'{e}el and dimer state. We find that the coherent part of the opticalabsorption for $V=0$ is given by a single peak at $\omega=U$ and broad but weakabsorption 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 anappreciable nearest neighbor interaction $V>W/2$ almost all spectral weight istransferred to the $\Delta q_C=0$-exciton and the $\Delta q_C=\pi/a$-excitonwhose relative spectral weights very sensitively depend on both the lattice andthe spin dimerization of the ground state.