Exact results for the optical absorption of strongly correlated electrons in a half-filled Peierls-distorted chain
In this second of three articles on the optical absorption of electrons in a half-filled Peierls-distorted chain we present exact results for strongly correlated tight-binding electrons. In the limit of a strong on-site interaction $U$ we map the Hubbard model onto the Harris-Lange model which can be solved exactly in one dimension in terms of spinless fermions for the charge excitations. The exact solution allows for an interpretation of the charge dynamics in terms of parallel Hubbard bands with a free-electron dispersion of band-width $W$, separated by the Hubbard interaction $U$. The spin degrees of freedom enter the expressions for the optical absorption only via a momentum dependent but static ground state expectation value. The remaining spin problem can be traced out exactly since the eigenstates of the Harris-Lange model are spin-degenerate. This corresponds to the Hubbard model at temperatures large compared to the spin exchange energy. Explicit results are given for the optical absorption in the presence of a lattice distortion $δ$ and a nearest-neighbor interaction $V$. We find that the optical absorption for $V=0$ is dominated by a peak at $ω=U$ and broad but weak absorption bands for $| ω-U | \leq W$. For an appreciable nearest-neighbor interaction, $V>W/2$, almost all spectral weight is transferred to Simpson's exciton band which is eventually Peierls-split.