Towards entanglement entropy of random large-N theories

A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the notion of shifted Matsubara frequency to compute von Neumann and Renyi entanglement entropies for generic bipartitioning of such systems. We argue that the von Neumann entropy can be computed from equilibrium spectral functions without partitioning, while the Renyi entropy requires recalculating the spectrum in the interacting case. We demonstrate the flexibility of the method by applying it to examples of a two-site problem in presence of decoherence and coupled Sachdev-Ye-Kitaev models.