  Leveraging the decomposability of the fast Fourier transform, I propose a new
class of tensor network that is efficiently contractible and able to represent
many-body systems with local entanglement that is greater than the area law.
Translationally invariant systems of free fermions in arbitrary dimensions as
well as 1D systems solved by the Jordan-Wigner transformation are shown to be
exactly represented in this class. Further, it is proposed that these tensor
networks be used as generic structures to variationally describe more
complicated systems, such as interacting fermions. This class shares some
similarities with Evenbly & Vidal's branching MERA, but with some important
differences and greatly reduced computational demands.
