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