Zero frequency divergence and gauge phase factor in the optical response theory

The static current-current correlation leads to the definitional zero frequency divergence (ZFD) in the optical susceptibilities. Previous computations have shown nonequivalent results between two gauges (${\bf p\cdot A}$ and ${\bf E \cdot r}$) under the exact same unperturbed wave functions. We reveal that those problems are caused by the improper treatment of the time-dependent gauge phase factor in the optical response theory. The gauge phase factor, which is conventionally ignored by the theory, is important in solving ZFD and obtaining the equivalent results between these two gauges. The Hamiltonians with these two gauges are not necessary equivalent unless the gauge phase factor is properly considered in the wavefunctions. Both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models of trans-polyacetylene serve as our illustrative examples to study the linear susceptibility $\chi^{(1)}$ through both current-current and dipole-dipole correlations. Previous improper results of the $\chi^{(1)}$ calculations and distribution functions with both gauges are discussed. The importance of gauge phase factor to solve the ZFD problem is emphasized based on SSH and TLM models. As a conclusion, the reason why dipole-dipole correlation favors over current-current correlation in the practical computations is explained.Comment: 17 pages, 7 figures, submitted to Phys. Rev.

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

The analytical solutions for the third-harmonic generation (THG) on infinite chains in both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models of trans-polyacetylene are obtained through the scheme of dipole-dipole ($DD$) correlation. They are not equivalent to the results obtained through static current-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) in THG may not be directly explained by the single electron models.Comment: 10 pages, 4 figures, submitted to Phys. Rev.