an atomless cavity. We found in such a periodic lattice the critical point that occurs in a single Dicke model becomes a critical region that is periodically changing with the wavenumber k. In the weak-coupling normal phase of the system we observed a flat band and its corresponding localization that can be controlled by the ground-state SPT. Our work builds the connection between flat band physics and SPT, which may fundamentally broaden the regimes of many-body theory and quantum optics.