Boundary-induced dynamics and quantum memory effect of 1D and 2D topological systems

The dynamics after a change of the boundary condition for selected 1D and 2D topological systems are analyzed. We consider the 1D Su-Schrieffer-Heeger (SSH) model and Kitaev model transforming from periodic to open boundary condition and the 2D Chern insulator (CI) and topological quadrupole insulator (TQI) transforming from a cylinder or Mobius strip to open boundary condition. In all the cases, we found the occupation of the topological edge states reaches a steady-state value after the transformation is completed in absence of any external dissipation mechanism. The steady-state value depends on the ramping rate of the boundary condition. The dependence of the steady-state occupation of the topological edge states on the ramping rate thus exemplifies one kind of quantum memory effect, which originates from the trapping of excitations due to the localized nature of the edge states. The mechanism suggests that this type of quantum memory effect may be universal in topological systems with localized edge states.