A simple but quite non-trivial class of non-equilibrium processes of a quantum many-body system is quantum quenches. We start with a ground state \(\mid \!\Phi _{0}\rangle\) of a certain Hamiltonian H0. At time t = 0, we suddenly change the Hamiltonian from H0 to a new one H. The original state \(\mid \!\Phi _{0}\rangle\) no longer stays at the ground state and starts to experience the time evolution for t > 0. Such a process is called a quantum quench. In particular, when the Hamiltonian changes homogeneously over the whole space, it is called a global quench [131, 132, 133], while if the change is localized in a certain small region, it is called a local quench [134].