# Exact solution for the quench dynamics of a nested integrable system

## TL;DR

This paper develops an exact method to analyze the non-equilibrium quench dynamics of nested integrable systems, specifically the spin-1 Lai-Sutherland model, revealing detailed steady-state and entanglement propagation characteristics.

## Contribution

It extends the Quench Action approach to nested integrable models, providing explicit solutions for the post-quench steady state and entanglement dynamics in the spin-1 Lai-Sutherland model.

## Key findings

- Characterized the post-quench steady state for the model.
- Predicted entanglement and mutual information propagation patterns.

## Abstract

Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has been focusing on models with an elementary (i.e., not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the Quench Action approach. Specifically, we consider the spin-$1$ Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.