Nonlocal correlations and spectral properties of the Falicov-Kimball model

Understand

We derive an analytical expression for the local two-particle vertex of the Falicov-Kimball model, including its dependence on all three frequencies, the full vertex and all reducible vertices.

• This allows us to calculate the self energy in diagrammatic extensions of dynamical mean field theory, specifically in the dual fermion and the one-particle irreducible approach.
• Non-local correlations are thence included and originate here from charge density wave fluctuations.
• At low temperatures and in two dimensions, they lead to a larger self energy contribution at low frequencies and a more insulating spectrum.