Adiabatic quenches through an extended quantum critical region

By gradually changing the degree of the anisotropy in an 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 antiferromagnetic phase. By means of time-dependent density matrix renormalization group 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 to the predictions of the Kibble- Zurek and Landau-Zener theories.