Excitons in the strong coupling limit of the one-dimensional extended Hubbard model

Abstract

Excitons in the strong coupling limit of the half-filled one-dimensional extended Hubbard model with $1/r$ interactions are studied. Unlike the situation for nearest neighbor interactions, where there is at most only one (doubly degenerate) bound state, a $1/r$ interaction results in an infinite number of doubly degenerate bound states. In the continuum limit the exciton states are one-dimensional hydrogenlike states, with binding energies $\ensuremath{\sim}{1/n}^{2}.$ The particle--hole separation grows rapidly with n as ${n}^{2}.$ The binding energies are reduced on a discrete lattice. However, for conjugated systems of interest, the discrete correction to the continuum limit are small. When the infinite onsite repulsion limit is relaxed the degenerate states split, forming a doublet of even and odd parity states.