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

Fourier transform of fermionic systems and the spectral tensor network