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The analytical solutions for the third-harmonic generation (THG) on infinitechains in both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) modelsof trans-polyacetylene are obtained through the scheme of dipole-dipole ($DD$)correlation. They are not equivalent to the results obtained through staticcurrent-current ($J_0J_0$) correlation or under polarization operator$\hat{P}$. The van Hove singularity disappears exactly in the analytical forms,showing that the experimentally observed two-photon absorption peak (TPA) inTHG may not be directly explained by the single electron models.Comment: 10 pages, 4 figures, submitted to Phys. Rev.

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