Entanglement and localization transitions in eigenstates of interacting chaotic systems

TL;DR

This paper investigates how entanglement and localization in eigenstates of interacting chaotic systems transition rapidly from weak to strong as interaction strength increases, using entropy measures and inverse participation ratio.

Contribution

It introduces a universal exponential model for entanglement transition and derives an exact relationship linking localization and purity in such systems.

Findings

Entanglement measures follow a simple exponential transition.

Universal behavior observed across different entropy measures.

Derived relationship connects localization with purity.

Abstract

The entanglement and localization in eigenstates of strongly chaotic subsystems are studied as a function of their interaction strength. Excellent measures for this purpose are the von-Neumann entropy, Havrda-Charv{\' a}t-Tsallis entropies, and the averaged inverse participation ratio. All the entropies are shown to follow a remarkably simple exponential form, which describes a universal and rapid transition to nearly maximal entanglement for increasing interaction strength. An unexpectedly exact relationship between the subsystem averaged inverse participation ratio and purity is derived that infers the transition in the localization as well.