Quantum chaos and entanglement in ergodic and non-ergodic systems

TL;DR

This paper investigates how entanglement entropy reflects quantum chaos in ergodic and non-ergodic systems, revealing its potential as a chaos indicator and its relation to classical chaos measures.

Contribution

It demonstrates that entanglement entropy signals chaos in quantum systems and explores its connection to classical chaos measures like Kolmogorov-Sinai entropy.

Findings

EE indicates global chaos in ergodic systems

EE can be maximized in non-ergodic systems with local chaos

Quantum KAM tori correspond to low entanglement entropy

Abstract

We study entanglement entropy (EE) as a signature of quantum chaos in ergodic and non-ergodic systems. In particular we look at the quantum kicked top and kicked rotor as multi-qubit systems, and investigate the single qubit EE which characterizes bipartite entanglement of this qubit with the rest of the system. We study the correspondence of the Kolmogorov-Sinai entropy of the classical kicked systems with the EE of their quantum counterparts. We find that EE is a signature of global chaos in ergodic systems, and local chaos in non-ergodic systems. In particular, we show that EE can be maximised even when systems are highly non-ergodic, when the corresponding classical system is locally chaotic. In contrast, we find evidence that the quantum analogue of Kolmogorov-Arnol'd-Noser (KAM) tori are tori of low entanglement entropy. We conjecture that entanglement should play an important role in any quantum KAM theory.