  The Kondo effect is an 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 fidelity susceptibility approach by using it to identify the crossover
and quantum phase transitions in the one and two impurity Anderson models.
