QUROPE Quantum Information Processing and Communication in Europe

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 describe more complicated systems, possibly leading to highly-efficient calculations in the Fermi-liquid phase. This class shares some similarities with Evenbly & Vidal's branching MERA, but with some important differences and greatly reduced computational demands.