Dynamical Freezing of Response in Driven Many-Body Quantum System

We show, that the response of a periodically driven quantum many- body system may freeze drastically, when driven with certain combinations of driving parameters (amplitude and frequency). We demonstrate this effect with analytical results for a broad class of integrable quantum spin models (illustrated particularly for one-dimensional Transverse Ising Model)and direct numerical integration data for large system-size. We show that the immunity of the freezing behavior to external noise can be controlled arbitrarily by controlling the strength of the local (on-site) field.