Auxiliary particle theory of threshold singularities in photoemission and X-ray absorption spectra: Test of a conserving T-matrix approximation

TL;DR

This paper develops a many-body slave particle approach to calculate threshold singularities in photoemission and X-ray spectra, demonstrating that the conserving T-matrix approximation accurately reproduces known power-law behaviors across different coupling regimes.

Contribution

It introduces a conserving slave particle T-matrix approximation for analyzing threshold singularities, unifying photoemission and X-ray absorption spectra calculations within a single framework.

Findings

Numerical results match exact infrared power-law behavior.

The approach works in both weak and strong coupling regimes.

Establishes a relation between CTMA and parquet equations.

Abstract

We calculate the exponents of the threshold singularities in the photoemission spectrum of a deep core hole and its X-ray absorption spectrum in the framework of a systematic many-body theory of slave bosons and pseudofermions (for the empty and occupied core level). In this representation, photoemission and X-ray absorption can be understood on the same footing; no distinction between orthogonality catastrophe and excitonic effects is necessary. We apply the conserving slave particle T-matrix approximation (CTMA), recently developed to describe both Fermi and non-Fermi liquid behavior systems with strong local correlations, to the X-ray problem as a test case. The numerical results for both photoemission and X-ray absorption are found to be in agreement with the exact infrared powerlaw behavior in the weak as well as in the strong coupling regions. We point out a close relation of the CTMA with the parquet equation approach of Nozi{\`e}res et al.