Single-boson exchange decomposition for the extended Hubbard model with application to the optical conductivity

Abstract

The parquet decomposition has proven a versatile tool to compute properties of strongly interacting quantum many-body systems. While it captures vertex corrections unbiased with respect to the scattering channel, it is mainly limited by the vast size of the working variables. Recently, a reformulation of the parquet equations in terms of single-bosonexchange diagrams has been put forward. For the Hubbard model, it has already been confirmed that this reduces the memory requirements and thus facilitates the application to larger systems. In order to use this method in the extended Hubbard model, the single-boson exchange decomposition is generalized to nonlocal interactions. In the process, the main working variables are analyzed using diagrammatic arguments and numerical results for the benzene ring in exact diagonalization. By comparing the Hubbard model to its extended counterpart, we discovered that the nonlocal interaction is responsible for the slow convergence of the Hedin equation because the vertex functions display less trivial large-frequency behavior. Furthermore, the parquet and single-boson exchange decomposition are applied to the current-current correlation function. The results show that especially $\pi$-tons, i.e. special polaritons in the transversal particle-hole channel, are relevant for the interaction of light with strongly correlated materials. The formation of the $\pi$-ton quasiparticles seems to be caused by magnetic and density fluctuations.