Abstract
A remarkable feature of quantum many-body systems is the orthogonality catastrophe that 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.
Highlights
Introduction.—Numerous many-body systems exhibit properties and phases that cannot be explained in exclusively classical terms
We show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, that any quenched quantum many-body system, whose variance in ground state energy scales with the system size, exhibits the orthogonality catastrophe
In the limit of large N the local perturbation forces the system to assume an orthogonal state—an effect known as orthogonality catastrophe (OC)
Summary
Introduction.—Numerous many-body systems exhibit properties and phases that cannot be explained in exclusively classical terms. A remarkable feature of quantum many-body systems is the orthogonality catastrophe that describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics.
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