Exciton condensation in bilayer spin-orbit insulator

We investigate the nature of the magnetic excitations of a bilayer single-orbital Hubbard model in the intermediate-coupling regime. This model exhibits a quantum phase transition (QPT) between a paramagnetic (PM) and an insulating antiferromagnetic (AFM) phase at a critical value of the coupling strength. By using the random phase approximation, we show that the QPT is continuous when the PM state is a band insulator and that the corresponding quantum critical point (QCP) arises from the condensation of preformed excitons. These low-energy excitons reemerge on the other side of the QCP as the transverse and longitudinal modes of the AFM state. In particular, the longitudinal mode remains sharp for the model parameters relevant to Sr$_{3}$Ir$_{2}$O$_{7}$ because of the strong easy-axis anisotropy of this material.