Generic Optical Excitations of Correlated Systems: π -tons

Abstract

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]

Single-boson exchange decomposition of the vertex function

“…where s and t denote the singlet and triplet channel. We insert the decomposition (18) of the singlet vertex f s and obtain the desired relation for the particle-hole notation, which is equation (19) in the main text and we summarized all U -pp-irreducible contributions into the vertex,…”

“…We relate the left-and right-sided Hedin vertices λ α andλ α . To do this, we use the following relation for the vertex function that holds under time-reversal symmetry combined with SU(2) symmetry [12], We combine this with equations (9) and (19) to obtain a relation for the irreducible vertices ϕ,…”

“…The traditional formulation of diagrammatic theories based on two-particle quantities poses however significant challenges. One of them is the immense algorithmic complexity of the parquet equations [13], which re-stricts direct numerical applications to impurity models [9,10,12,14] and small clusters [15][16][17][18][19][20]. Furthermore, the perturbation theory based on the two-particle self-energy has revealed fundamental problems which have received much attention in the context of nonperturbative approaches, such as the dynamical meanfield theory (DMFT) [3].…”

“…These are indications that the partitioning of the full vertex defined by the parquet equations is not in general useful to define effective quantities. Interestingly, useful information can however be extracted from this representation when it is possible to identify an effective particle [19]. On the other hand, the full vertex function itself does retain the physical meaning of an effective interaction [29] which implies that, for example, it allows a fluctuation diagnostic of the single-particle self-energy [30,31].…”

Parquetlike equations for the Hedin three-leg vertex

“…It is indeed possible to solve the parquet equations on a small lattice [38,39,[43][44][45], which also allows the application of the full DΓA scheme to transport phenomena. This reveals a significant effect of strong antiferromagnetic fluctuations on the optical conductivity [46]. However, due to the severe restrictions on the lattice size it is not possible to study the effect of long-ranged correlations on transport properties.…”