  Quench spectroscopy is a relatively new method which enables the
investigation of spectral properties of many-body quantum systems by monitoring
the out-of-equilibrium dynamics of real-space observables after a quench. So
far the approach has been devised for global quenches or using local
engineering of momentum-resolved excitations. Here, we extend the quench
spectroscopy method to local quenches. We show that it allows us to extract
quantitative information about global properties of the system, and in
particular the elementary excitation spectrum. Using state-of-the-art numerical
methods, we simulate the out-of-equilibrium dynamics of a variety of quantum
systems following various local quench protocols and demonstrate a general
scheme for designing an appropriate local quench protocol for any chosen model.
We provide detailed examples of how the local quench protocol can be realised
in realistic current generation experiments, including ultracold atomic gases
and trapped ion systems.
