Operator entanglement entropy of the time evolution operator in chaotic systems

TL;DR

This paper investigates how the operator entanglement entropy evolves in various quantum systems, revealing universal growth patterns and saturation behaviors that reflect information propagation in chaotic, localized, and Floquet systems.

Contribution

It introduces a mapping of operator EE to a global quench problem, providing a unified understanding of its growth and saturation across different many-body systems.

Findings

Power law growth of operator EE at weak disorder

Logarithmic growth of operator EE at strong disorder

Saturation values match those of random unitary operators (Page value)

Abstract

We study the growth of the operator entanglement entropy (EE) of the time evolution operator in chaotic, many-body localized and Floquet systems. In the random field Heisenberg model we find a universal power law growth of the operator EE at weak disorder, a logarithmic growth at strong disorder, and extensive saturation values in both cases. In a Floquet spin model, the saturation value after an initial linear growth is identical to the value of a random unitary operator (the Page value). We understand these properties by mapping the operator EE to a global quench problem evolved with a similar parent-Hamiltonian in an enlarged Hilbert space with the same chaotic, MBL and Floquet properties as the original Hamiltonian. The scaling and saturation properties reflect the spreading of the state EE of the corresponding time evolution. We conclude that the EE of the evolution operator should characterize the propagation of information in these systems.