Central Charge of the Parallelogram Lattice Strong Coupling Schwinger Model

We put forth a Fierz-transformed hopping expansion for strong coupling Wilson fermions. As an application, we show that the strong coupling Schwinger model on parallelogram lattices with nonbacktracking Wilson fermions span, as a function of the lattice skewness angle, the Δ=-1 critical line of six-vertex models. This Fierz-transformed formulation also applies to backtracking Wilson fermions, which as we describe apparently correspond to richer systems. However, we have not been able to identify them with exactly solved models.