Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit

TL;DR

This paper links the orthogonality catastrophe in quantum many-body systems to the quantum speed limit, showing that systems with energy variance scaling with size exhibit this phenomenon, demonstrated in Fermi gases and spin models.

Contribution

It establishes a fundamental connection between the orthogonality catastrophe and the quantum speed limit, providing a new theoretical framework for understanding sensitivity in quantum systems.

Findings

Orthogonality catastrophe occurs in systems with energy variance scaling with size.

The dynamics can be characterized by the quantum speed limit.

Demonstrated in trapped Fermi gas and Lipkin-Meshkov-Glick model.

Abstract

A remarkable feature of quantum many-body systems is the orthogonality catastrophe which describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system whose variance in ground state energy scales with the system size exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems -- the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model.