Entanglement in coupled kicked tops with chaotic dynamics

TL;DR

This paper investigates how entanglement in two coupled chaotic quantum systems transitions from unentangled to highly entangled states, revealing universal scaling laws and confirming them through numerical and perturbative analyses.

Contribution

It introduces a universal scaling parameter governing entanglement transition in coupled chaotic systems and validates this universality across different symmetry classes and subsystem sizes.

Findings

Universal scaling describes entanglement transition.

Level spacing statistics match random matrix predictions.

Entanglement entropy follows a universal scaling law.

Abstract

The entanglement of eigenstates in two coupled, classically chaotic kicked tops is studied in dependence of their interaction strength. The transition from the non-interacting and unentangled system towards full random matrix behavior is governed by a universal scaling parameter. Using suitable random matrix transition ensembles we express this transition parameter as a function of the subsystem sizes and the coupling strength for both unitary and orthogonal symmetry classes. The universality is confirmed for the level spacing statistics of the coupled kicked tops and a perturbative description is in good agreement with numerical results. The statistics of Schmidt eigenvalues and entanglement entropies of eigenstates is found to follow a universal scaling as well. Remarkably this is not only the case for large subsystems of equal size but also if one of them is much smaller. For the entanglement entropies a perturbative description is obtained, which can be extended to large couplings and provides very good agreement with numerical results. Furthermore, the transition of the statistics of the entanglement spectrum towards the random matrix limit is demonstrated for different ratios of the subsystem sizes.