Deterministic chaos and fractal entropy scaling in Floquet CFT

TL;DR

This paper investigates how periodic driving in 2d Floquet conformal field theory induces fractal features in entanglement entropy scaling, especially near chaos transition, revealing complex dynamical behavior.

Contribution

It introduces the study of fractal entropy scaling in Floquet CFT driven by logistic or tent maps, linking chaos theory with quantum entanglement.

Findings

Fractal features emerge in entanglement entropy under chaotic driving.

Logistic map driving causes highly oscillatory entanglement entropy.

Fractal contributions dominate entropy scaling near chaos transition.

Abstract

In this paper, 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 highly oscillating function of the subsystem size.