Entanglement detection in quantum materials with competing orders

We investigate entanglement detection in quantum materials through criteria based on the simultaneous suppression of collective matter excitations. Unlike other detection schemes, these criteria can be applied to continuous and unbounded variables. By considering a system of interacting dipoles on a lattice, we show the detection of collective entanglement arising from two different physical mechanisms, namely, the ferroelectric ordering and the dressing of matter degrees of freedom by light. In the latter case, the detection shows the formation of a collective entangled phase not directly related to spontaneous symmetry breaking. These results open a new perspective for the entanglement characterization of competing orders in quantum materials and have direct application to quantum paraelectrics with large polariton splittings.