We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the AdS/CFT correspondence, we identify transitions between types of von Neumann operator algebras throughout the phase diagram. We find transitions of the form II1 <-> III <-> I-infinity that reduce to II1 <-> I-infinity in the strongly interacting limit, where they connect nonfactorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model.
