  Quantum phase transitions are highly remarkable phenomena manifesting in
quantum many-body systems. However, their precise identifications in
equilibrium systems pose significant theoretical and experimental challenges.
Thus far, dynamical detection protocols employing global quantum quenches have
been proposed, wherein transitions are discerned from global nonequilibrium
excitations. In this work, we demonstrate that quantum phase transitions can be
detected through localized out-of-equilibrium excitations induced by local
quantum quenches. While the resulting dynamics after the quench are influenced
by both the local quench operation and the intrinsic dynamics of the quantum
system, the effects of the former are exclusively extracted through the
cutting-edge framework called quantum reservoir probing (QRP). Through the QRP,
we find that the impacts of the local quenches vary across different quantum
phases and are significantly suppressed by quantum fluctuations amplified near
quantum critical points, thereby precisely delineating phase boundaries. We
demonstrate that the QRP can detect quantum phase transitions in the
paradigmatic integrable and nonintegrable quantum systems, and even topological
quantum phase transitions, all within the identical framework employing
single-site observables.
