R\'enyi Entropy Singularities as Signatures of Topological Criticality in Coupled Photon-Fermion Systems

We establish the relation between topological phase (TP) transitions and quantum entropy singularities in a Kitaev chain embedded in a cavity. Even though both the von Neumann and Renyi entanglement entropies between light and matter sub-systems display singularities at the TP transition, we show that remarkably the Renyi entropy is analytically connected to the measurable photon Fano factor. Thus, we put forward a path to experimentally access the control and detection of a TP phase transition via a Renyi entropy analysis.