title: Fourier transform for 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 the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands.
authors.affiliation: Département de Physique, Université de Sherbrooke, Québec J1K 2R1, Canada; ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, 08860 Barcelona, Spain; and Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Ferris