Dynamical signature of localization-delocalization transition in a one-dimensional incommensurate lattice

We investigate the quench dynamics of a one-dimensional incommensurate lattice described by the Aubry-Andre model by a sudden change of the strength of incommensurate potential Delta and unveil that the dynamical signature of localization-delocalization transition can be characterized by the occurrence of zero points in the Loschmidt echo. For the quench process with quenching taking place between two limits of Delta = 0 and Delta = infinity, we give analytical expressions of the Loschmidt echo, which indicate the existence of a series of zero points in the Loschmidt echo. For a general quench process, we calculate the Loschmidt echo numerically and analyze its statistical behavior. Our results show that if both the initial and post-quench Hamiltonian are in extended phase or localized phase, Loschmidt echo will always be greater than a positive number; however if they locate in different phases, Loschmidt echo can reach nearby zero at some time intervals.