Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains

TL;DR

This paper investigates how kicked quantum chaotic spin-1/2 chains deviate from expected random matrix entanglement statistics, revealing that their eigenstate entanglement distribution differs significantly due to tensor-product Hilbert space structure.

Contribution

It demonstrates that kicked spin-1/2 chains deviate from random matrix predictions in eigenstate entanglement distribution, highlighting limitations of standard random matrix models for such systems.

Findings

Eigenstate entanglement approaches random matrix results in average.

Distribution of eigenstate entanglement differs significantly from random matrix predictions.

Deviations are attributed to tensor-product structure of Hilbert spaces.

Abstract

It is commonly expected that for quantum chaotic many body systems, the statistical properties approach those of random matrices when increasing the system size. We demonstrate for various kicked spin-1/2 chain models that the average eigenstate entanglement indeed approaches the random matrix result. However, the distribution of the eigenstate entanglement differs significantly. While for autonomous systems such deviations are expected, they are surprising for the more scrambling kicked systems. Similar deviations occur in a tensor-product random matrix model with all-to-all interactions. Therefore, we attribute the origin of the deviations for the kicked spin-chain models to the tensor-product structure of the Hilbert spaces. As a consequence, this would mean that such many body systems cannot be described by the standard random matrix ensembles.