In this talk, I built upon the identification of matchgates with Gaussian fermionic tensors to discuss a Hamiltonian description of 2D matchgates tensor networks with an open physical boundary. I develop an analytic understanding of a phase transition in the latter, that has previously been found numerically. In doing so, I encounter a correspondence between a many-body topological phase transition in a Z_2 gauge theory (toric code) and a topological single-particle transition in a class D superconductor. In a second step, I consider random matchgate tensor networks and discuss when and how an ensemble of tensor networks can be described by a non-linear super matrix model.