Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model

TL;DR

This paper investigates the dynamical behavior of the Lipkin-Meshkov-Glick model during a quantum phase transition, combining numerical simulations with classical and quantum transition models to better understand the underlying physical processes.

Contribution

It introduces a novel quantum transition model that improves upon classical approaches, providing deeper insights into the dynamics of the LMG model during phase transitions.

Findings

Numerical results show pronounced effects of spectral avoided level crossings.

A classical transition model approximates the numerical dynamics.

A refined quantum transition model enhances understanding of the evolution.

Abstract

It is of high interest, in the context of Adiabatic Quantum Computation, to better understand the complex dynamics of a quantum system subject to a time-dependent Hamiltonian, when driven across a quantum phase transition. We present here such a study in the Lipkin-Meshkov-Glick (LMG) model with one variable parameter. We first display numerical results on the dynamical evolution across the LMG quantum phase transition, which clearly shows a pronounced effect of the spectral avoided level crossings. We then derive a phenomenological (classical) transition model, which already shows some closeness to the numerical results. Finally, we show how a simplified quantum transition model can be built which strongly improve the classical approach, and shed light on the physical processes involved in the whole LMG quantum evolution. From our results, we argue that the commonly used description in term of Landau-Zener transitions is not appropriate for our model.