Nonlocal correlations and spectral properties of the Falicov-Kimball model

TL;DR

This paper derives an analytical expression for the local two-particle vertex in the Falicov-Kimball model, enabling the inclusion of non-local correlations in advanced many-body calculations, revealing increased insulating behavior at low temperatures.

Contribution

It provides the full frequency-dependent local two-particle vertex for the Falicov-Kimball model, facilitating improved diagrammatic extensions of dynamical mean field theory.

Findings

Non-local correlations increase the self energy at low frequencies.

Spectral properties show more insulating behavior at low temperatures.

Charge density wave fluctuations drive non-local correlations.

Abstract

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.