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.

We derive the improved estimators for general interactions and employ these for the continuoustime quantum Monte Carlo method. Using a worm algorithm we show how measuring higher-ordered correlators leads to an improved high-frequency behavior in irreducible quantities such as the oneparticle self-energy or the irreducible two-particle vertex for non-density-density interactions. A good knowledge of the asymptotics of the two-particle vertex is essential for calculating non-local electronic correlations using diagrammatic extensions to the dynamical mean field theory as well as for calculating susceptibilities. We test our algorithm against analytic results for the multi-orbital atomic-limit and the Falicov-Kimball model.

The interaction of light with solids gives rise to new bosonic quasiparticles, with the exciton being-undoubtedly-the most famous of these polaritons. While excitons are the generic polaritons of semiconductors, we show that for strongly correlated systems another polariton is prevalentoriginating from the dominant antiferromagnetic or charge density wave fluctuations in these systems. As these are usually associated with a wave vector (π, π, . . .) or close to it, we propose to call the derived polaritons π-tons. These π-tons yield the leading vertex correction to the optical conductivity in all correlated models studied: the Hubbard, the extended Hubbard model, the Falicov-Kimball, and the Pariser-Parr-Pople model, both in the insulating and in the metallic phase. arXiv:1902.09342v2 [cond-mat.str-el]

We investigate the influence of self-energy diagrams beyond the two-particle vertex level within dual fermion theory. Specifically, we calculate the local three-particle vertex and construct from it selected dual fermion self-energy corrections to dynamical mean field theory. For the two-dimensional Hubbard model, the thus obtained self-energy corrections are small in the parameter space where dual fermion corrections based on the two-particle vertex only are small. However, in other parts of the parameter space, they are of a similar magnitude and qualitatively different from standard dual fermion theory. The high-frequency behavior of the self-energy correction is -surprisingly -even dominated by corrections stemming from the three-particle vertex.

Many-body calculations for multi-orbital systems at present typically employ Slater or Kanamori interactions which implicitly assume a full rotational invariance of the orbitals, whereas the real crystal has a lower symmetry. In cubic symmetry, the low-energy t2g orbitals have an on-site Kanamori interaction, albeit without the constraint U = U + 2J implied by spherical symmetry (U : intraorbital interaction, U : inter-orbital interaction, J: Hund's exchange). Using maximally localized Wannier functions we show that deviations from the standard, spherically symmetric interactions are indeed significant for 5d orbitals (∼ 25% for BaOsO 3 ; ∼ 12% if screening is included), but less important for 3d orbitals (∼ 6% for SrVO 3 ; ∼ 1% if screened).