Dynamical characterization of topological phases beyond the minimal models

Dynamical characterization of topological phases under quantum quench dynamics has been demonstrated as a powerful and efficient tool. Previous studies have focused on systems which the Hamiltonian consists matrices that commute with each other satisfy Clifford algebra. In this work, we consider Hamiltonians are beyond minimal model. Specifically, two types layered is studied, consisting do not all We find terms anti-commute others can hold common band-inversion surfaces, controls topology bands, but for terms, there no universal behavior need to be treated case by case.