Disorder-induced dynamical Griffiths singularities after certain quantum quenches

The properties of matter in thermal equilibrium can be largely affected by atypical and rare spatial disorder configurations due to inhomogeneities. They induce Yang-Lee-Fisher zeros in the partition function which are arbitrarily close to the real-temperature (or field) axis. In simpler words, the partition function becomes a non-analytical function: a phenomenon known as Griffiths singularities. We demonstrate that those same rare regions produce a dynamical analogue of this phenomenon on closed quantum systems. As a consequence, certain observables become non-analytical functions of time after certain quantum quenches. We show that the non-analyticities occur already at the early-time stages of the unitary evolution, and are due to quantum-quench-induced excitations localized inside those rare regions. We finally discuss on the strength of the singularities associated to the non-analyticities, and on their numerical and experimental signatures.