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 prevalent-originating 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.
Local n-particle vertex functions represent the crucial ingredient for diagrammatic extensions of dynamical mean field theory (DMFT). Hitherto their application has been restricted-with a few ...exceptions-to the n=2-particle vertex while higher-order vertices have been neglected. In this paper we derive a general analytical expression for the local n-particle (one-particle-reducible) vertex of the Falicov-Kimball model (FKM). We observe that the magnitude of such vertex functions itself strongly increases with the number of particles n. On the other hand, their effect on generic Feynman diagrams remains rather moderate due to the damping effect of the Green's functions present in such diagrams. Nevertheless, they yield important contributions to the self-energy corrections calculated in diagrammatic extensions of DMFT as we explicitly demonstrate using the example of dual-fermion calculations for the two-dimensional FKM at quarter filling of the stationary f electrons. Here corrections to the self-energy obtained from the three-particle vertex are indeed comparable in magnitude to corresponding corrections stemming from the two-particle vertex.
In the Falicov-Kimball model, a model for (annealed) disorder, we expect weak localization corrections to the optical conductivity. However, we get such weak localization effects only when employing ...a pp-ladder approximation in the dual fermion approach. In the full parquet approach, these pp contributions are suppressed by ph-reducible diagrams. For the optical conductivity, we find that the ph¯ channel yields the main contribution, even in the region where weak localization in the pp ladder was indicated.
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. Nonlocal 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 continuous-time 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 one-particle 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 nonlocal 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 multiorbital atomic limit and the Falicov-Kimball model.
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 t sub(2)g orbitals have an on-site Kanamori interaction, albeit without the constraint U = U' + 2J implied by spherical symmetry (U is the intra-orbital interaction, U' is the interorbital interaction, J is 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 sub(3); ~ 12% if screening is included) but are less important for 3d orbitals (~ 6% for SrVO sub(3); ~ 1% if screened).
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