# Correlation and entanglement spreading in nested spin chains

## TL;DR

This paper numerically investigates correlation and entanglement spreading in nested integrable spin chains, specifically the Lai-Sutherland model, validating theoretical predictions about quasiparticle dynamics and light-cone velocities after quantum quenches.

## Contribution

It provides the first direct numerical validation of Bethe ansatz and quasiparticle predictions in nested integrable systems like the Lai-Sutherland model.

## Key findings

- Confirmed the quasiparticle-based formula for entanglement growth.
- Validated Bethe ansatz predictions for correlation light-cone velocity.
- Demonstrated the effectiveness of DMRG and exact diagonalization in nested systems.

## Abstract

The past few years have witnessed the development of a comprehensive theory to describe integrable systems out of equilibrium, in which the Bethe ansatz formalism has been tailored to address specific problems arising in this context. While most of the work initially focused on the study of prototypical models such as the well-known Heisenberg chain, many theoretical results have been recently extended to a class of more complicated $\it{nested}$ integrable systems, displaying different species of quasiparticles. Still, in the simplest context of quantum quenches, the vast majority of theoretical predictions have been numerically verified only in systems with an elementary Bethe ansatz description. In this work, we fill this gap and present a direct numerical test of some results presented in the recent literature for nested systems, focusing in particular on the Lai-Sutherland model. Using time-dependent density matrix renormalization group and exact diagonalization methods, we compute the spreading of both correlation functions and entanglement entropy after a quench from a simple class of product initial states. This allows us to test the validity of the nested version of a conjectured formula, based on the quasiparticle picture, for the growth of the entanglement entropy, and the Bethe ansatz predictions for the "light-cone" velocity of correlation functions.