Binding energy of ${1\mathrm{B}}_{\mathrm{u}}$ singlet excitons in the one-dimensional extended Hubbard-Peierls model

Using a symmetrized density-matrix renormalization-group formulation, we have investigated the electronic binding energy of the lowest optically allowed exciton (${1\mathrm{B}}_{\mathrm{u}}$) within an extended Hubbard-Peierls model (with parameters U, V, and δ) for conjugated chains with N=80 sites. Three symmetries, the ${\mathrm{C}}_2$, spin parity, and electron-hole symmetries, have been applied to construct the projector operator. Analysis of our results on the ratios between exciton binding energies and exciton energies, sheds light on the current experimental and theoretical controversy on exciton binding for polyacetylene and polyparaphenylene vinylene. We show that in the absence of dimerization, the exciton binding energy is vanishingly small for U/t up to 5 and V/t up to 2.3; for a finite dimerization, it is only when V is large enough that the exciton gets to be significantly bound. This result questions the applicability to conjugated polymers of the strong correlation picture, in which the exciton binding energy is equal to V.