# Orthogonality catastrophe in Coulomb systems

## TL;DR

This paper investigates the orthogonality catastrophe in Coulomb systems, incorporating dynamic screening effects, and finds that traditional approximations overestimate decay exponents, with implications for understanding impurity behavior in metals.

## Contribution

It systematically addresses the OC problem for Coulomb interactions, including dynamic screening, finite impurity mass, and challenges previous assumptions of non-interacting fermions.

## Key findings

- Dynamic screening alters decay exponents significantly.
- Screened Coulomb potential yields larger exponents than static models.
- Finite impurity mass results in small but finite impurity residues.

## Abstract

The orthogonality catastrophe (OC) problem is considered solved for 50 years. It has important consequences for numerous dynamic phenomena in fermionic systems, including Kondo effect, X-ray spectroscopy, and quantum diffusion of impurities, and is often used in the context of metals. However, the key assumptions on which the known solution is based---impurity potentials with finite cross-section and non-interacting fermions---are both highly inaccurate for problems involving charged particles in metals. As far as we know, the OC problem for the "all Coulomb" case has never been addressed systematically, leaving it unsolved for the most relevant practical applications. In this work we include effects of dynamic screening in a consistent way and demonstrate that for short-range impurity potentials the non-interacting Fermi-sea approximation radically overestimates the power-law decay exponent of the overlap integral. We also find that the dynamically screened Coulomb potential leads to a larger exponent than the often used static Yukawa potential. Finally, by employing the Diagrammatic Monte Carlo technique, we quantify effects of a finite impurity mass and reveal how OC physics leads to small, but finite, impurity residues.