Exotic freezing of response in a 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 $\left(\omega \right)$ 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 nonmonotonic 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.

Figure 1

(Color online) (a) $m^z$ vs $t$ (numerical, $N={10}^4$, and $h_0=10$) for various $\omega \text{s}$. (b) $Q$ vs $2h_0/\omega$ for $h_0=20$, 30, and 40, compared with the analytical formula $Q=\frac{1}{1+\left|J_0\left(2h_0/\omega \right)\right|}$ [Eq. (7)]. The peaks $P_1$, $P_2$, and $P_3$ representing maximal freezing, corresponds to three zeros of $J_0\left(\frac{2h_0}{\omega }\right)$, occurring at $\frac{2h_0}{\omega }=5.520,\dots ,8.653,\dots ,11.971,\dots$, respectively. (c) $Q$ vs $h_0$ for $\omega ⪡1$ (numerical). The peaks are smoothed out yielding a roughly monotonic behavior. (d) The counterclassical trend of stronger freezing for higher $h_0$ is demonstrated with single-sweep results; we plot $Q_s=\frac{1}{T}{\int }_0^T{m}^z\left(t\right)dt$, (where $T=2\pi /\omega$) for $N=100$. The figure also demonstrates monotonic adiabatic to nonadiabatic transition at low $\omega$ regime for different $h_0$.