  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.
