Driving CFT into the world of black holes, deterministic chaos and fractal dimensions

We study 2d Floquet conformal field theory, where the external periodic driving is described by iterated logistic or tent maps. These maps are known to be typical examples of dynamical systems exhibiting the order-chaos transition, and we show that, as a result of such driving, the entanglement entropy scaling develops fractal features when the corresponding dynamical system approaches the chaotic regime. For the driving set by the logistic map, fractal contribution to the scaling dominates, making entanglement entropy a highly oscillating function of the subsystem size.