Quantum fidelity of the Aubry-André model and the exponential orthogonality catastrophe

Advances in experimental tools allow to study quantum fidelity unprecedented controlled settings. While the metals, when adding a local impurity, is well known show Anderson orthogonality catastrophe (AOC), there remain outstanding questions other phases and Here, we aim tackle these by exploring systematically ground-state of Fermi liquid (extended) Aubry-Andr\'e (AA) model, which allows explore AOC both localized extended critical phases. We discover that typically exponential regime AA model at mobility edge for an while it decays with power law weak single-site impurity. explain this terms correlations multipoint correlations. The OC found be insulating regime, due fundamentally different, statistical mechanism, explained detail. Furthermore, consider parametric perturbation find numerically, agreement analytical derivation provide here.