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.

What are the experimentally observable effects of vertex corrections in superconductors?

We calculate the effects of vertex corrections, of non-constant density of states and of a (self-consistently determined) phonon self-energy for the Holstein model on a 3D cubic lattice. We replace vertex corrections with a Coulomb pseudopotential, mu*, adjusted to give the same Tc, and repeat the calculations, to see which effects are a distinct feature of vertex corrections. This allows us to determine directly observable effects ofvertex corrections on a variety of thermodynamic properties of superconductors. To this end, we employ conserving approximations (in the local approximation) to calculate the superconducting critical temperatures, isotope coefficients, superconducting gaps, free-energy differences and thermodynamic critical fields for a range of parameters. We find that the dressed value of lambda is significantly larger than the bare value. While vertex corrections can cause significant changes in all the above quantities (even whenthe bare electron-phonon coupling is small), the changes can usually be well-modeled by an appropriate Coulomb pseudopotential. The isotope coefficient proves to be the quantity that most clearly shows effects of vertex corrections that can not be mimicked by a mu*.Comment: 28 pages, 12 figure