On the X-ray-Problem in the Falicov-Kimball model in large dimensions at half-filling

The f-electron spectral function of the Falicov-Kimball model is calculated within the dynamical mean-field theory using the numerical renormalization group method as the impurity solver. Both the Bethe lattice and the hypercubic lattice are considered at half filling. For small U we obtain a single-peaked f-electron spectral function, which --for zero temperature-- exhibits an algebraic (X-ray) singularity ($|\omega|^{-\alpha}$) for $\omega \rightarrow 0$. The characteristic exponent $\alpha$ depends on the Coulomb (Hubbard) correlation U. This X-ray singularity cannot be observed when using alternative (Keldysh-based) many- body approaches. With increasing U $\alpha$ decreases and it vanishes for sufficiently large U when the f-electron spectral function develops a gap and a two-peak structure (metal-insulator transition).