Fidelity Susceptibility Perspective on the Kondo Effect and Impurity Quantum Phase Transitions

The Kondo effect is a ubiquitous phenomenon appearing at low temperature in quantum confined systems coupled to a continuous bath. Efforts in understanding and controlling it have triggered important developments across several disciplines of condensed matter physics. A recurring pattern in these studies is that the suppression of the Kondo effect often results in intriguing physical phenomena such as impurity quantum phase transitions or non-Fermi-liquid behavior. We show that the fidelity susceptibility is a sensitive indicator for such phenomena because it quantifies the sensitivity of the system's state with respect to its coupling to the bath. We demonstrate the power of the fidelity susceptibility approach by using it to identify the crossover and quantum phase transitions in the one and two impurity Anderson models. The feasibility of measuring fidelity susceptibility in condensed matter as well as ultracold quantum gases experiments opens exciting new routes to diagnose the Kondo problem and impurity quantum phase transitions.