On X-ray-singularities in the f-electron spectral function of the Falicov-Kimball model

TL;DR

This paper investigates the X-ray singularities in the f-electron spectral function of the Falicov-Kimball model using dynamical mean-field theory and numerical renormalization group, revealing how the singularity depends on Coulomb interaction U.

Contribution

It provides the first detailed analysis of the X-ray singularity in the Falicov-Kimball model's spectral function within DMFT using NRG, highlighting the U-dependent behavior of the singularity.

Findings

At small U, spectral function shows an algebraic singularity at zero temperature.

The singularity exponent decreases with increasing U and vanishes in the insulating phase.

The singularity is not observable with Keldysh-based approaches.

Abstract

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 $\omega \to 0$. 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).