Molecular-exciton approach to spin-charge crossovers in dimerized Hubbard and excitonic chains.

Abstract

The crossover from band to correlated states in half-filled quantum cell models is studied in a molecular-exciton framework based on a chain of dimers. Crystal states with one or several excited dimers yield analytical excitation energies to first order in interdimer Coulomb interactions V(p,p') for excitonic chains or interdimer electron transfer ${\mathit{t}}_{\mathrm{\ensuremath{-}}}$=t(1-\ensuremath{\delta}) for Hubbard chains. Molecular-exciton analysis of excitations and transition moments rationalizes exact numerical solutions of oligomers with arbitrary intradimer correlations U, ${\mathit{V}}_{1}$, and electron transfer ${\mathit{t}}_{+}$=t(1+\ensuremath{\delta}), including the number, positions, and transition moments of low-lying excitations. Short correlation lengths of infinite chains with large alternation \ensuremath{\delta}\ensuremath{\ge}0.6 lead to converged crystal states for oligomers containing N=4--7 dimers. The present approach provides a detailed picture of excited-state crossovers with increasing U, ${\mathit{V}}_{1}$, and V(p,p'). Quite generally, the lowest singlet excitation ${\mathit{S}}_{1}$ is one-photon allowed (1B) on the band side of the spin-charge crossover and two-photon allowed (2A) on the correlated side. Intermediate correlations and large \ensuremath{\delta} reveal different crossovers in Hubbard chains, where 1B involves charge transfer between dimers, and excitonic chains, where 1B has an excited dimer.We also obtain two-photon transition moments M and extend vanishing M(2A) in the band limit up to U=2${\mathit{t}}_{+}$, the \ensuremath{\delta}\ensuremath{\sim}1 crossover of Hubbard chains. We find finite M(2A) on the correlated side, however, where 2A contains two triplet dimers in either alternating Hubbard or excitonic chains. Their different spin-charge crossovers appear as an abrupt and continuous increase, respectively, of two-photon intensity on going from the correlated to the band side. The greater delocalization (\ensuremath{\delta}\ensuremath{\sim}0.07--0.33) realized in conjugate polymers is consistent with excitonic chains. The potential V(p,p') in the Pariser-Parr-Pople model for conjugated hydrocarbons distinguishes strongly fluorescent polymers with ${\mathit{S}}_{1}$=1B from others with ${\mathit{S}}_{1}$=2A. We also relate our results at large \ensuremath{\delta} to other approximations for nonlinear optical spectra of conjugated polymers.