Parquet approximation for molecules: Spectrum and optical conductivity of the Pariser-Parr-Pople model

We study a simple model system for the conjugated $\pi$-bonds in benzene, the Pariser-Parr-Pople (PPP) model, within the parquet approximation (PA), exemplifying the prospects of the PA for molecules. Advantages are the polynomial scaling of the PA with the number of orbitals, and the natural calculation of one- and two-particle spectral functions as well as of response and correlation functions. We find large differences in the electronic correlations in the PPP model compared to a Hubbard model with only local interactions. The quasiparticle renormalization (or mass enhancement) is much weaker in the PPP than in the Hubbard model, but the static part of the self-energy enhances the band gap of the former. Furthermore, the vertex corrections to the optical conductivity are much more important in the PPP model. Because non-local interactions strongly alter the self-energy, we conclude that the PA is more suitable for calculating conjugated $\pi$-bonds in molecules than single site dynamical mean-field theory.