Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

TL;DR

This paper investigates the adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model across its quantum critical point, analyzing residual energy and entanglement entropy to understand diabatic effects during the transition.

Contribution

It provides a Landau-Zener approximation for the finite size LMG model and analyzes its effectiveness in describing residual energy behavior during quantum quenches.

Findings

Landau-Zener approximation successfully reproduces residual energy trends

Residual energy depends on the transition rate and system size

Entanglement entropy analysis supports the dynamical behavior observed

Abstract

The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model across its quantum critical point is studied. The dynamics is realized by linearly switching the transverse field from an initial large value towards zero and considering different transition rates. We concentrate our attention on the residual energy after the quench in order to estimate the level of diabaticity of the evolution. We discuss a Landau-Zener approximation of the finite size LMG model, that is successful in reproducing the behavior of the residual energy as function of the transition rate in the most part of the regimes considered. We also support our description through the analysis of the entanglement entropy of the evolved state. The system proposed is a paradigm of infinite-range interaction or high-dimensional models.