Statistics of orthogonality catastrophe events in localised disordered lattices

TL;DR

This paper investigates the statistical orthogonality catastrophe in disordered insulators, analyzing how local perturbations affect many-body ground states in Anderson and Aubry-André models, revealing model-specific features and experimental prospects.

Contribution

It provides a comprehensive statistical analysis of orthogonality events in disordered lattices, highlighting differences between models and proposing experimental verification methods.

Findings

Distinct orthogonality event statistics in Anderson and Aubry-André models

Unexpected features in Aubry-André model due to quasi-periodic potential

Proposed experimental setups for observing orthogonality catastrophe

Abstract

We address the phenomenon of statistical orthogonality catastrophe in insulating disordered systems. More in detail, we analyse the response of a system of non-interacting fermions to a local perturbation induced by an impurity. By inspecting the overlap between the pre and post-quench many-body ground states we fully characterise the emergent statistics of orthogonality events as a function of both the impurity position and the coupling strength. We consider two well-known one-dimensional models, namely the Anderson and the Aubry- Andr\'e insulators, highlighting the arising differences. Particularly, in the Aubry-Andr\'e model the highly correlated nature of the quasi periodic potential produces unexpected features in how the orthogonality catastrophe occurs. We provide a quantitative explanation of such features via a simple, effective model. We further discuss the incommensurate ratio approximation and suggest a viable experimental verification in terms of charge transfer statistics and interferometric experiments using quantum probes.