Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

We study the adiabatic dynamics of the Lipkin-Meshkov-Glick (LMG) model close to its quantum critical point by linearly switching the transverse field from an initial large value to zero. We concentrate our attention on the residual energy after the quench in order to characterize the level of diabaticity of the evolution. As a function of the characteristic time of the quench tau we identify three different regimes. For fast quenches the residual energy E-res is almost independent on tau. For slower quenches a second intermediate region appears in which a powerlike decay emerges with E-res similar to tau(-3/2). By further slowing the quench rate, we find a third large-tau regime characterized by a different power law, E-res similar to tau(-2). All these findings can be accounted for by means of an effective Landau-Zener approximation for the finite-size LMG model. We complete our description of the adiabatic dynamics of the LMG model through the analysis of the entanglement entropy of the evolved state.