Multipartite Entanglement in Crossing the Quantum Critical Point

TL;DR

This paper studies how multipartite entanglement evolves during slow quantum quenches crossing a critical point in the quantum Ising and Lipkin-Meshkov-Glick models, revealing scaling behaviors consistent with the Kibble-Zurek mechanism.

Contribution

It demonstrates how quantum Fisher information quantifies multipartite entanglement dynamics and shows the influence of long-range physics in different quantum models during phase transitions.

Findings

Quantum Fisher information density scales as a power law with quench rate.

Scaling conforms to the Kibble-Zurek mechanism with small corrections.

Long-range behaviors affect entanglement scaling in local systems.

Abstract

We investigate the multipartite entanglement for a slow quantum quench crossing a critical point. We consider the quantum Ising model and the Lipkin-Meshkov-Glick model, which are local and full-connected quantum systems, respectively. The multipartite entanglement is quantified by quantum Fisher information with the generator defined as the operator of the ferromagnetic order parameter. The quench dynamics begins with a ground state in a paramagnetic phase, and then the transverse field is driven slowly to cross a quantum critical point, and ends with a zero transverse field. For the quantum Ising model, based on methods of matrix product states, we calculate the quantum Fisher information density of the final state. Numerical results of both linear and nonlinear quenches show that the quantum Fisher information density of the final state scales as a power law of the quench rate, which overall conforms to the prediction of the Kibble-Zurek mechanism with a small correction. We show that this correction results from the long-range behaviors. We also calculate the quantum Fisher information density in the Lipkin-Meshkov-Glick model. The results show that the scaling of quantum Fisher information in this full-connected system conforms to the Kibble-Zurek mechanism better, since the long-range physics cannot be defined in this nonlocal system. Our results reveal that the multipartite entanglement provides an alternative viewpoint to understand the dynamics of quantum phase transitions, specifically, the nontrivial long-range physics.