Adiabatic quenches through an extended quantum critical region
  By gradually changing the degree of the anisotropy in a XXZ chain we study the defect formation in a quantum system that crosses an extended critical region. We discuss two qualitatively different cases of quenches, from the antiferromagnetic to the ferromagnetic phase and from the critical to the antiferromegnetic phase. By means of time-dependent DMRG simulations, we calculate the residual energy at the end of the quench as a characteristic quantity gauging the loss of adiabaticity. We find the dynamical scalings of the residual energy for both types of quenches, and compare them with the predictions of the Kibble-Zurek and Landau-Zener theories. 
Franco Pellegrini, Simone Montangero, Giuseppe E. Santoro, Rosario   Fazio