Fourier transform of fermionic systems and the spectral tensor network

Abstract

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.

Accepted in Phys. Rev. Lett. 9 pages, 13 figures. This version is reorganized to be more pedagogical and includes a new derivation of the FFT decomposition, as well as extra details on the contraction scheme in the Appendix

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