Yang, SJ (reprint author), Beijing Normal Univ, Dept Phys, Beijing 100875, Peoples R China.
We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps which indicate non trivial topological structures. The Chern numbers with respect to the Bloch vector and the potential shift angle are computed. In the limit of the continuous model, the Chern number of each band is exactly one We demonstrate that the particle number pumped by the adiabatically shift of the potential is directly related to the topological invariants. (C) 2014 Elsevier B.V. All rights reserved.