# Quantum information scrambling after a quantum quench

## TL;DR

This paper investigates how quantum information spreads in non-equilibrium many-body systems after a quantum quench, using mutual information as a diagnostic, and compares integrable and non-integrable models.

## Contribution

It introduces mutual information scaling as a new diagnostic for quantum information scrambling post-quench in one-dimensional systems.

## Key findings

- Integrable systems show algebraic decay of mutual information, indicating weak scrambling.
- Non-integrable systems exhibit faster decay, indicating stronger scrambling.
- Quasiparticle lifetime influences the decay rate in non-integrable models.

## Abstract

How quantum information is scrambled in the global degrees of freedom of non-equilibrium many-body systems is a key question to understand local thermalization. Here we propose that the scaling of the mutual information between two intervals of fixed length as a function of their distance is a diagnostic tool for scrambling after a quantum quench. We consider both integrable and non-integrable one dimensional systems. In integrable systems, the mutual information exhibits an algebraic decay with the distance between the intervals, signalling weak scrambling. This behavior may be qualitatively understood within the quasiparticle picture for the entanglement spreading, predicting, in the scaling limit of large intervals and times, a decay exponent equal to $1/2$. Away from the scaling limit, the power-law behavior persists, but with a larger (and model-dependent) exponent. For non-integrable models, a much faster decay is observed, which can be attributed to the finite life time of the quasiparticles: unsurprisingly, non-integrable models are better scramblers.