F-electron spectral function of the Falicov-Kimball model in infinite dimensions: the half-filled case

The $f$-electron spectral function of the Falicov-Kimball model is calculated via a Keldysh-based many-body formalism originally developed by Brandt and Urbanek. We provide results for both the Bethe lattice and the hypercubic lattice at half filling. Since the numerical computations are quite sensitive to the discretization along the Kadanoff-Baym contour and to the maximum cutoff in time that is employed, we analyze the accuracy of the results using a variety of different moment sum rules and spectral formulas. We find that the $f$-electron spectral function has interesting temperature dependence, becoming a narrow single-peaked function for small $U$ and developing a gap, with two broader peaks for large $U$.