  Long-lived single-frequency oscillations in the local non-equilibrium
dynamics of a quantum many-body system is an exceptional phenomenon. In fact,
till now, it has never been observed, nor predicted, for the physically
relevant case where a system is prepared to be quenched from one quantum phase
to another. Here we show how the quench dynamics of the entanglement spectrum
may reveal the emergence of such oscillations in a correlated quantum system
with Kondo impurities. The oscillations we find are characterized by a single
frequency. This frequency is independent of the amount of energy released by
the local quench, and scales with the inverse system size. Importantly, the
quench-independent frequency manifests itself also in local observables, such
as the spin-spin correlation function of the impurities.
