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Fermionic tensor network methods
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We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor network methods for fermionic lattice systems in a local way, avoiding the need of a Jordan-Wigner transformation or the explicit tracking of leg crossings by swap gates in 2D tensor networks. The graded Hilbert spaces can be readily integrated with other internal and lattice symmetries in tensor networks, and only require minor extensions to an existing tensor network software package. We review and benchmark the fermionic versions of common algorithms for matrix product states and projected entangled-pair states.
Forward citations
Cited by 2 Pith papers
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Graphical Calculus for Fermionic Tensors
A parity-aware graphical calculus extends the ZX diagram language to fermionic modes, covering Gaussian states, partial traces, purification, fermionization/bosonization, and fermionic error-correcting codes.
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Les Houches Lecture Notes on Tensor Networks
A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.
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