摘要
We classify the topology of the quench dynamics by homotopy groups. A relation between the topological invariant of a postquench order parameter and the topological invariant of a static Hamiltonian is shown in d + 1 dimensions (d = 1,2,3). The midgap states in the entanglement spectrum of the postquench states reveal their topological nature. When a trivial quantum state is under a sudden quench to a Chern insulator, the midgap states in the entanglement spectrum form rings. These rings are analogous to the boundary Fermi rings in the Hopf insulators. Finally, we show a postquench order parameter in 3+1 dimensions can be characterized by the second Chern number. The number of Dirac cones in the entanglement spectrum is equal to the second Chern number.