Stabilizer entropy in non-integrable quantum evolutions

TL;DR

This paper investigates how entanglement and stabilizer entropy evolve in quantum many-body systems after a quench, revealing differences between free-fermion and non-integrable models in their long-term behavior.

Contribution

It provides a comparative analysis of entanglement and stabilizer entropy dynamics in integrable versus non-integrable quantum spin chains.

Findings

Free-fermion models show a gap in long-time stabilizer entropy.

Non-integrable models saturate stabilizer entropy to random matrix theory values.

Distinct behaviors in entanglement spectrum anti-flatness between models.

Abstract

Entanglement and stabilizer entropy are both involved in the onset of complex behavior in quantum many-body systems. Their interplay is at the root of complexity of simulability, scrambling, thermalization and typicality. In this work, we study the dynamics of entanglement, stabilizer entropy, and the anti-flatness of the entanglement spectrum after a quantum quench in a spin chain. We find that free-fermion theories show a gap in the long-time behavior of these resources compared to their random matrix theory value while non-integrable models saturate it.