Bound polariton states in the Dicke-Ising model

We present a study of hybrid light-matter excitations in cavity QED materials using the Dicke-Ising model as a theoretical framework. Leveraging linear response theory, we derive the exact excitations of the system in the thermodynamic limit. Our results demonstrate that the cavity can localize spin excitations, leading to the formation of bound polaritons, where the cavity acts as an impurity of the two-excitation band, localizing spin-wave pairs around single-spin domains. We derive the condition for the existence of these bound states and discuss its satisfiability in different regimes. Finally, we show that these effects persist in finite systems using exact-diagonalization calculations.