Entangling power of time-evolution operators in integrable and nonintegrable many-body systems

TL;DR

This paper investigates how entanglement measures evolve in quantum many-body systems, revealing that integrable and chaotic systems exhibit similar entanglement growth, but differ in their entangling power, with spectral correlations playing a key role.

Contribution

It provides an analytical comparison of entanglement growth in integrable and nonintegrable systems, highlighting the role of spectral correlations and revealing unexpected similarities.

Findings

Ballistic growth of entanglement in integrable models

Exponential saturation of linear entropy in integrable systems

Nonintegrable systems have lower maximum entangling power

Abstract

The entangling power and operator entanglement entropy are state independent measures of entanglement. Their growth and saturation is examined in the time-evolution operator of quantum many-body systems that can range from the integrable to the fully chaotic. An analytically solvable integrable model of the kicked transverse field Ising chain is shown to have ballistic growth of operator von Neumann entanglement entropy and exponentially fast saturation of the linear entropy with time. Surprisingly a fully chaotic model with longitudinal fields turned on shares the same growth phase, and is consistent with a random matrix model that is also exactly solvable for the linear entropy entanglements. However an examination of the entangling power shows that its largest value is significantly less than the nearly maximal value attained by the nonintegrable one. The importance of long-range spectral correlations, and not just the nearest neighbor spacing, is pointed out in determing the growth of entanglement in nonintegrable systems. Finally an interesting case that displays some features peculiar to both integrable and nonintegrable systems is briefly discussed.