Deterministic chaos and fractal entropy scaling in Floquet conformal field theories

Dmitry S Ageev,Askar A Iliasov,Andrey A Bagrov

doi:10.1103/physrevb.103.l100302

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.

Highlights

In this Letter, we study two-dimensional 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
A natural playground to address the dynamics of periodically modulated correlated systems is the framework of Floquet conformal field theories (CFTs)

Summary

Holomorphic dynamics of iterated maps

Dynamical systems defined by the iterative composition of simple maps are known to exhibit chaos, bifurcations, and self-organization phenomena. For many standard choices of the holomorphic maps, the evolution of the corresponding dynamical system generates fractals. Treating the Floquet driving of a CFT as a dynamical system, which can manifest chaotic or fractal properties on the level of map iterations, does not correspond to the common approach normally taken in quantum chaos theory [35,36]. In this Letter, we report that periodic Floquet modulation based on a certain choice of iterated holomorphic maps can evoke fractal patterns of quantum correlations in the driven state. It leads to the emergence of an exotic class of quantum states with

Published by the American Physical Society

Sreg log