Analytical solutions to the third-harmonic generation in trans-polyacetylene: Application of dipole-dipole correlation to single-electron models

The analytical solutions of the third-harmonic generation (THG) for infinit e chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki model of trans-polyacetylene are obtained through the scheme of dipole-dipole (DD) c orrelation. They are not equivalent to the results obtained through static current-current (J(0)J(0)) correlation or under polarization operator (P) o ver cap with the same initial distribution functions. Physical backgrounds for those differences are analyzed qualitatively. The van Hove singularity disappears exactly in analytical forms under DD correlation, showing that t he experimentally observed two-photon absorption peak (TPA) in THG cannot b e directly explained by the single-electron models. Our analytical results on TPA are consistent with numerical computations using dipole formulas.