  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 R\'enyi entanglement entropies for generic bi-partitioning of such
systems. We argue that the von Neumann entropy can be computed from equilibrium
spectral functions w/o partitioning, while the R\'enyi entropy requires
re-calculating 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.
