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 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.