Exciton binding energy in the strong correlation limit of conjugated chains

By applying the numerically accurate symmetrized density-matrix renormalization-group method coupled with the extended Hubbard-Peierls model, we find that (i) the on-site Hubbard repulsion energy U dramatically reduces the binding energy of the lowest optically allowed ${1B}_u$ exciton; (ii) in the zero-dimerization limit, there exists a critical value of V at which the ${1B}_u$ exciton becomes bound; the critical value $V_c=2t$ is fully in agreement with the recent analytical results at the infinite-U limit by Gallagher and Mazumdar [Phys. Rev. B 56, 15 025 (1997)], furthermore, this critical value decreases appreciably for weaker on-site correlation strengths, when the dimerization amplitude $\left(\delta \right)$ is nonzero. The present accurate numerical results contradict those obtained recently by Yu, Saxena, and Bishop [Phys. Rev. B 56, 3697 (1997)] both qualitatively and quantitatively. We also present first-order perturbation plus random-phase-approximation and single configuration-interaction analyses to rationalize the numerical calculations.