Exotic Freezing of Response in Quantum Many-Body System

We show that when a quantum many-body system is subjected to coherent periodic driving, the response may exhibit exotic freezing behavior in high driving frequency ($\omega$) regime. In a periodically driven classical thermodynamic system, freezing at high $\omega$ occurs when $1/\omega$ is much smaller than the characteristic relaxation time of the system, and hence the freezing always increases there as $\omega$ is increased. Here, in the contrary, we see surprising non-monotonic freezing behavior of the response with $\omega$, showing curious peak-valley structure. Quite interestingly, the entire system tends to freeze almost absolutely (the freezing peaks) when driven with a certain combination of driving parameters values (amplitude and $\omega$) due to coherent suppression of dynamics of the quantum many-body modes, which has no classical analog. We demonstrate this new freezing phenomenon analytically (supported by large-scale numerics) for a general class of integrable quantum spin systems.