Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state

Understand

We study a class of periodically driven $d-$dimensional integrable models and show that after $n$ drive cycles with frequency $\omega$, pure states with non-area-law entanglement entropy $S_n(l) \sim l^{\alpha(n,\omega)}$ are generated, where $l$ is the linear dimension of the subsystem, and $d-1 \le \alpha(n,\omega) \le d$.

• We identify and analyze the crossover phenomenon from an area ($S \sim l^{ d-1}$ for $d\geq1$) to a volume ($S \sim l^{d}$) law and provide a criterion for their occurrence which constitutes a generalization of Hastings' theorem to driven integrable systems in one dimension.
• We also find that $S_n$ generically decays to $S_{\infty}$ as $(\omega/n)^{(d+2)/2}$ for fast and $(\omega/n)^{d/2}$ for slow periodic drives; these two dynamical phases are separated by a topological transition in the eigensprectrum of the Floquet Hamiltonian.
• This dynamical transition manifests itself in the temporal behavior of all local correlation functions and does not require a critical point crossing during the drive.