EXACT RESULTS FOR THE OPTICAL-ABSORPTION OF STRONGLY CORRELATED ELECTRONS IN A HALF-FILLED PEIERLS-DISTORTED CHAIN

In this, the second of three articles on the optical absorption of ele ctrons in a half-filled Peierls-distorted chain, we present exact resu lts for strongly correlated tight-binding electrons. In the limit of a strong on-site interaction U, we map the Hubbard model onto the Harri s-Lange model which can be solved exactly in one dimension in terms of spinless fermions for the charge excitations. The exact solution allo ws for an interpretation of the charge dynamics in terms of parallel H ubbard bands with a free-electron dispersion of bandwidth W, separated by the Hubbard interaction U. The spin degrees of freedom enter the e xpressions for the optical absorption only via a momentum-dependent bu t static ground-state expectation value. The remaining spin problem ca n be traced out exactly since the eigenstates of the Harris-Lange mode l are spin degenerate. This corresponds to the Hubbard model at temper atures large compared with the spin exchange energy. Explicit results are given for the optical absorption in the presence of a lattice dist ortion delta and a nearest-neighbour interaction V. We find that the o ptical absorption for V = 0 is dominated by a peak at omega = U and br oad but weak absorption bands for \omega - U\ less than or equal to W. For an appreciable nearest-neighbour interaction V > W/2, almost all the spectral weight is transferred to Simpson's exciton band which is eventually Peierls split.