# Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model

## TL;DR

This paper studies how excited state quantum phase transitions influence the nonadiabatic dynamics in the Lipkin-Meshkov-Glick model, revealing state-dependent scaling behaviors and validating mean-field approaches in the thermodynamic limit.

## Contribution

It demonstrates the impact of excited state quantum phase transitions on dynamics and confirms mean-field methods accurately capture scaling near these transitions.

## Key findings

- Scaling properties depend on energy eigenstates.
- Mean-field dynamics match exact results in the thermodynamic limit.
- Excited state quantum phase transitions significantly affect nonadiabatic behavior.

## Abstract

We theoretically investigate the impact of the excited state quantum phase transition on the adiabatic dynamics for the Lipkin-Meshkov-Glick model. Using a time dependent protocol, we continuously change a model parameter and then discuss the scaling properties of the system especially close to the excited state quantum phase transition where we find that these depend on the energy eigenstate. On top, we show that the mean-field dynamics with the time dependent protocol gives the correct scaling and expectation values in the thermodynamic limit even for the excited states.