X-ray singularities in the f-electron spectral function of the Falicov-Kimball model -: art. no. 125101

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 (vertical bar omega vertical bar(-alpha)) for omega -> 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 vanishes for sufficiently large U when the f-electron spectral function develops a gap and a two-peak structure (metal-insulator transition).